I heated my small non-stick skillet over medium heat and added one large sliced shallot. I let it caramelize for about 5 minutes, then chopped up the meat from on roasted chicken leg quarter and added it to the carmelizing shallot. I let those go for 5 more minutes, then dumped in about 1/8 a cup of bbq sauce (use whatever you have- I had Sweet Baby Ray's Spicy) and the juice of half a lemon. I turned the heat on low and walked away. Actually- "Diners, Drive-ins and Dives" was coming on and I like that show. I let it sit and slowly bubble for probably 45 minutes. Do you have to do that? No. Am I glad I did it? Yes. The bbq sauce got reduced and glazed the pieces of chicken. There were little bits of crunchy, charred sauce on the edges. Yum.
I took one 6" flour tortilla and put it in my cast iron skillet with already heated olive oil. I put the quesadilla on the bottom of the skillet and sprinkled on a fair amount of grated mozzarella cheese. I put the chicken mixture on that, and finished with more grated cheese. I cooked it over medium heat for about 5 minutes, then flipped it and let it go until the cheese on the other side was melted.
I plated it up with half a sliced avocado. The combination of the sweet, spicy, crunchy meat and tortilla with the creamy, cold avocado was life-changing. Seriously- make this soon!