^I think clarifying just how bad the effects are would be informative. Are we talking "it makes life genuinely unpleasant because I'm bloated and gassy" or merely "my weight goes up a pound or two, and it's back to where it was two days later." The former probably means you have an issue with wheat or gluten; the latter can be dealt with.
I don't really believe in the concept of a whole "cheat day" (promotes too much binging and kind of a weird relationship with food, IMO) - but I will say: I train "fasted" Monday-Friday (early in the morning), and I generally avoid wheat/gluten altogether. However, on Saturday mornings, I sleep in a little, walk to a nearby coffee shop, buy a paper, a cup of coffee, and (gasp!) a bagel-and-egg sandwich before going to the gym around 10 o'clock (instead of the M-F schedule, 6 AM). I allow this special indulgence because that's usually the day I'll be going to the gym with intent of setting PR's, and I want to be well-rested, well-fueled, and readyb to rock.
If you want to be low-carb (in general) without giving up your favorite meal, one way to do it is making Friday night your enchilada night, and making Saturday your biggest gym day (i.e. the day you always try to set a new squat PR, or something like that).
The rules on this are different if you're trying to follow a purely ketogenic diet, in which case all carbs must be approached with caution. But I am guessing that's not you.
I would also note that you can have that entire meal without a tortilla. All of those goodies can be easily put into a frittata, or an omelette, or piled atop a bed of romaine, or just on a plate. I know it can be satisfying to have a "sandwich" or "burrito" or something to hold onto, but there's no rule against grilling your mushrooms, spinach, eggplant, zucchini, onions, and olives and dropping them on a plate topped with a nice dollop of sour cream and some sliced avocado.