Lay cling film over the chicken breasts and use a rolling pin, mallet or heavy pan to pound them to an even thickness. Don't flatten them so much they break apart.
Whisk together chipotle paste, olive oil, lime juice, smoked paprika, garlic powder, salt & black pepper in a large shallow dish. Coat the chicken and cover the bowl in cling film. Marinate in the fridge for as long as you have time for (up to overnight). If you're pushed for time just do 30 minutes at room temp.
In a small pot combine mayonnaise and sour cream with 1 tsp chipotle paste.
In a large non-stick pan over medium-high heat, fry the chicken for around 4 mins each side, or until lightly charred on the outside and white & piping hot through the centre. Remove and leave to rest to one side. Slice into strips just before needed.
Add the peppers and onion to the pan and fry until they begin to soften and lightly char, then remove them from the pan. Wipe/clean out the pan and place back on a medium heat.
Scatter half of the cheddar in the pan then lay a tortilla wrap on top. On one half, top with mozzarella, peppers & onion, avocado, chicken, and a drizzle of the chipotle sauce.
The cheese on the bottom will melt, then leak out oil, then turn a golden colour and crisp up. As it crisps, it'll attach itself to the wrap. Just try and gently press down on the wrap to remove any air bubbles. Once the cheese attaches to the wrap, use tongs to fold it over the fillings. This process should take around 4-5mins. Have faith - the cheese will attach as it crisps!
Remove and repeat with the second quesadilla, then slice in half and tuck in with more sauce if desired!