Like you said, the thing about teasing you have to know the person for awhile before the relationship gets to that point where teasing is acceptable. Even then some people don’t like it.
^^ This. Offer to give a demonstration on how to bake brownies or the like if she declines the contest. 
She is.
You’re actually not being a jerk at all. You’re not baking for the entire office and you have every right to exclude someone from outside your section if the whole point was to bring a treat for your co-workers/employees.
She’s a dick.
Mooching a goodie from someone you hardly know is grounds for copious thank yous and some sort of favor in the future. ASKING for more next time when you haven’t made any moves toward knowing the person better or repayment of first favor is tacky. Badgering you when you show up first thing for a THIRD mooch, and when told no for perfectly legit reasons, continuing to beg is just…not done.
As for what she said while doing all this, this is the rotten cherry on top. Don’t care if she’s just socially awkward. Nobody gets rewarded for bad behavior.
The ones I tease usually respond with a huge belly-laugh, and they give as good as they get. This doesn’t sound like the situation with Skald at all - if he was never laughing at my teasing, and looked kind of pissed-off, my teasing would end for him immediately; unlike the woman in the OP, I’m not a clueless git. 
That’s another thing. (Damn you edit time limit!)
If I had any kind of heart at all for this crap, I’d feel sorry for her that she’s never known what a beautiful thing it is to have a man be great in the kitchen. I have one of those. He doesn’t bake (that’s my thing sometimes) but he can make a delicious meal out of anything. I can’t.
She’s a sexist bitch. And a mooch. I hate people like that. I really hate people like her. I mean, seriously what is up with people who don’t believe what they are told about homemade things? I would make sure she never got another single piece of any baked good I brought into the office…ever. I would forbid my team for giving her some.
There’s not “bigger jerk” there’s just her - the jerk.
Give her a pass for the first instance and her sexist remark, but the second instance and remark was unacceptable and Skald should have made a quick reply telling her as much.
My bolding…Skald, Let this one go…give her the benefit of the doubt. She made an awkward comment (regardless of intention). You didn’t know her well and she didn’t know you well either.
Here would have been the time to set her straight and let her know how annoyed you are/were, and see if she apologizes or keeps up the sexist comments.
Had you addressed the situation on the second, you would absolutely know how to handle her this time.
But, she was/is the jerk.
Now, Dammit! PM a piece of cake!
I don’t blame you at all. As another man baker I understand the pride you take in your cooking, if it is not appreciated then give it to someone who does. Man to Man if you want my secret family recipe for cinnamon rolls I will give it to you via PM. My moms dentist gave her free dental care for 2 sheets of roll per visit. They have become locally famous around the neighborhood .
Good manners do not require you to give yummy food to people who insult you.
If this woman is actually a decent but clueless person, the ball is now in her court to apologize to you. No apology, no more goodies.
<holds out plate>
Can I have some cake?
They do require you not to deny a request in a manner that’s humiliating. Actually it should never have gotten to the point of Skald rejecting her request for cake. He should have stepped in and said “I don’t really like that kind of joking” but while handing over the cake.
Enough of the Homer Simpson quotes…
Give her the cake Skald, she’s teasing… but threaten to withhold the forthcoming triple chocolate cake if she gives the impression that she doesn’t believe you.
It’s nice to see you lot across The Pond using traditional English phrases… 
My vote: fuck her, and the horse she rode in on.
She is being a jerk. Skald, you’re doing the right thing, even if you’re being a little mean.
As I read this thread, I’m thinking of a tall, cold glass of milk to go with those brownies and cake. Skald, you claim your baking is good, but we won’t just take you at your word. Show us the evidence - let us decide!
She’s the jerk and she sounds like she’s a narcissist who thinks she’s the only person in the universe who can bake from scratch and has to put you in your place as not being able to bake from scratch, because you’re not allowed to be better than her at anything.
You should have made her admit you are a great baker in exchange for a piece of cake. I’d say you’re both being kind of jerky here. But in your defense, she started it. In her defense, you’re Skald.
Where did the milk come from? No man can make a glass of milk like that.
Except he didn’t deny her request in a manner that’s humiliating. He gave pretty much the answers I would expect from Judith Martin herself. Humiliating would have been if he’d loudly announced that he didn’t feed sexist bitchy mooches from other departments who repeatedly insulted him.
I doubt very much that Judith Martin would go along with this. Do you have any specific evidence of this?
I think Judith Martin would be okay with saying, “I can’t promise you that I’ll save a piece – after my team gets theirs, it’s only fair if it’s first-come, first-serve. But you’re welcome to stop by to see if there is any left.” Absent evidence otherwise, I don’t believe she would ever go along with this little swipe: “since she didn’t believe I could actually cook, I wouldn’t want to force her to pretend to like what I had made.” That’s an out-and-out rejection, and it’s gratuitous.
No, it’s not gatuitous or humiliating. She has insulted his baking on two occasions and called him a liar. ‘Nah, you wouldn’t want any of this crummy store-bought cake’ is a perfect response sends a pretty clear message.