I got some boneless, skinless chicken breasts out of the freezer. Turned out they’re actually pork chops. Whatever. I can buy chicken breasts. I want to attempt chicken cordon bleu for the first time. Seems simple enough. (I’ve never attempted Hollandaise, so I’ll cheat this time and concentrate on the chicken.)
What should I have with it? I’m thinking broccoli.
It’s a pretty rich/flavorful dish, I’d probably go with something on the blander side like rice (pilaf), broccoli sounds good too.
Broccoli would be good. But I’d pick asparagus as my first choice.
Asparagus is usually my first choice. I’ll have to think about it.
I recommend asparagus with hollandaise sauce.
Yes, asparagus is a better choice for Hollandaise.
The SO votes for asparagus. 
…I’ve never heard of putting Hollandaise on chicken cordon bleu.
Hollandaise in the blender or food processor is dead easy. I know purists think it’s cheating and there is something about blender hollandaise that, to a purist, is obviously lacking (you end up with paler hollandaise, maybe?!?), but that subtlety is lost on me.
This blog gives Julia Child’s recipe for blender hollandaise. If it was good enough for Julia, it’s good enough for me, by gum. Works just as well in a food processor.
I’ve never heard of putting hollandaise on chicken cordon bleu either, but it sounds yummy!
It goes on the asparagus, Julia.
Thanks for the recipe.
It sounded good, and I didn’t want to do a wine sauce.
I’ve not heard with any sauce on the Cordon Bleu, but after looking I see that it is included in some recipes.
I love Hollendaise and Asparagus but think it may be a bit much to have it on that and the Cordon Bleu. I would either leave it off of the chicken or have rice pilaf or a brown rice of some sort as a contrast.
…I would recommend an accompaniment of piano and violin; a full drum kit and horn section would overpower the dish 
Veg - something fresh and steamed that I could smoosh into the sauce for the chicken and it would taste great.
Starch - a hearty rice - because you get a piece of the CCB, the veg and then heap it with rice and the sauce, and…sorry, where was I?
I have the premade ones ($1 at the Jewel) once a week or so. I accompany it with a crusty roll and cranberry sauce.
I don’t have any cranberry sauce. Plenty of lingonberry jam, though.
I think I lived on those when I was student-living in Minneapolis. Except I accompanied it with Doritos.
I eventually undercooked one once and the slightly-gelatinous almost-raw chicken turned me off of them for years. Irrationally, I admit…it wasn’t the cordon bleu’s fault I wasn’t paying attention to the clock.
Asparagus marinated for 24 hours in a vinagrette salad dressing then grilled. Total nommage. Accompany with dirty rice.
Use mozzarella and procisutto instead of swiss cheese and bacon in your cordon bleu. As for side dishes, I agree with something bland. Rice and salad maybe, but it goes pretty well with anything, so just pick something you like.
I like something tart/sweet and bright on the plate to help balance out the richness and add color. The lingonberries sound good too.
I used to just put a ruffled lettuce leaf and a couple of little pickled apples on the plate to serve this purpose. Maybe that’s just getting a little too carried away if it’s just the two of you. You could throw a couple of strawberries or raspberries into a tossed salad for color.
I’ve made CCB with a light mushroom sauce but it’s really gilding the lily.
Wild rice and either warm asparagus with vinaigrette of a very simple tossed salad (again w/ vinaigrette). The wild rice is really the perfect starch, brown rice is a close second, and you’re going to want something like the vinaigrette to cut the richness.
And I agree with the other posters, lose the hollandaise.
Heretic!