Do you mean refined sugars and processed foods? I have a very low consumption of those foods for the same reason as you - migraines.
I generally only eat fruit, veg, meat, pulses, oats, rice and seafood. I don’t eat any bread, pasty or bakery type foods aside from the very rare treat. Mentally I find it just easier to limit myself to no processed foods and concentrate on getting variety within those categories.
I snack on raspberries, strawberries, carrots and apples. I shop every few days to make sure I always have some in the fridge.
Porridge oats and unsweetened almond milk for breakfast (or regular milk would work, I just don’t like the taste of milk!), or an apple if I’m in a rush.
Cold new potatoes are great for lunch and salads. Tinned tuna, frozen prawns (I buy the cheap ones and defrost in warm water, not sure if you’re supposed to do this), avocados, and those frozen baked potatoes you cook for 4 minutes in the microwave are all quick lunch ideas.
If I cook chicken or salmon for dinner I make extra to have for lunch the next day.
The cravings go within a week. I still get migraines around my period, but I only get about 1 in the second half of my cycle now.