Slice your peppers into small bits. Each bit should be about the size of your little fingernail. (Note: I say red peppers, but green, yellow, and orange are all great options too)
Add about 2/3 of the nut oil to a skillet or wok (my preference) on low-medium heat.
Add peppers, stir frequently so they don't burn.
Once your peppers have had a few minutes and are getting nice and soft, add your chicken.
Continue to stir frequently.
Once your chicken is nicely coated in oil, add your cayenne. Be sure to cover everything evenly.
Coat another skillet with the rest of your oil, then lay one tortilla on top
Sprinkle the cheese and salsa evenly across the tortilla.
Once the chicken is done, spread it over the top as well.
Toss the second tortilla on and cook on low heat.
Keep an eye on the bottom tortilla, it should start to brown nicely after a couple minutes.
Once it's brown you need to flip. (This can be a bit tricky. I tend to flip by placing a plate on top of the skillet and turning it around. I then use a pancake flipper to slide the quesadilla off the plate back onto the skillet.... I suspect it looks a bit dodgy while I'm doing it, but it works for me!)
Again, let the second tortilla brown. The cheese should melt nicely inside during this time.
Once brown, place on a plate and cut to desired sizes.