If they didn’t already have Peanut Brittle ice cream I would suggest something like that.
So I’ll say chocolate ice cream with raspberry infused chocolate chunks and a raspberry swirl and maybe throw some chashew pieces in there.
Or maybe root bear float ice cream with a marshmellow swirl and a root beer swirl.
Dark chocolate ice cream, with Oreo cookie chunks (big chunks, not just crumbs), and Maraschino cherries.
I’d totally buy that.
Great idea! But it the swirl needs to be really dark coffee, with extra caffeine, so that three bites = a normal cup of coffee.
Espresso ice cream with a butterscotch swirl. Call it “Espresso Yourself.”
Something berryflavored (with actual fruit bits) inside a concealing layer of vanilla.
No wait, berries and crushed almonds inside plain vanilla. That way I could name it “Suprise, I’m Nuts”. 
Chocolate ice cream with big veins of graham cracker crumbs, marshmallow (caramel and regular), caramel, fudge, and fudge chunks about the size of the phish in Phish Food. Kind of like S’mores, only…more.
Call it “S’most” 
I suppose it would be laced with Godiva liquer and be called Chocolate Martini, only because Dirty Martini ice cream is not appealing even to me.
In other news, the title of this thread just made me think “and I triiiiiiiiiiiiiiiiied to meeeeelt”, so maybe it would just be called “Nothing.”
Snappy answer.
Please send this idea straight to Ben and Jerry’s.
Dungeon Delight.
Black-and-blue ice cream, dotted with silver-dragée studs, with silver gummy handcuffs and black licorice cat-o’-nine-tails.
Anything but vanilla.
I have no idea what’s actually officially available via Ben & Jerry’s, but I’d look towards something like Banana Aniseed or French Vanilla Liquorice. Name? Um… Anisotropical.
There used to be one back in my homeland called Fish and Chips (chewy fish candy, and chocolate chip, in sea green mint ice cream) and I wish that was still around.
I may just have to try to make this now.
“We Brought Mandarin Chocolate Back Because It Was Little Nemo’s Favorite Flavor (And The Baskin-Robbins Version Sucks)”
Okay, it’s a little wordy and the Baskin-Robbins lawyers might have a problem with it. But you get the idea.
They used to have a Coconut Cream Pie flavor that was pretty similar to this. No cake batter though.
You know those Hershey’s kisses with air bubbles in them? Well, it’d be that but without the chocolate, and they’d call it, “Did You Hear Something?”
Santorum:
Creamy white sorbet, laced with dark chocolate.
You do realize that you are supposed to be describing an ice cream that commemorates you, right? 
Sweet cream base with all different kinds of salted nuts mixed in.
“Nuts, but Sweet”
This is almost exactly what I get at Cold Stone. Without the nuts. So sweet it’ll make your teeth tingle!