Strain and rinse the chickpeas, then add to a food processor. Pulse three to four times until the chickpeas are broken down a bit. Be careful not to overdo it; you want to preserve a bit of texture, not make hummus. You could also smash the chickpeas up a bit with a fork.
Melt butter (or heat olive oil) in a pan over medium heat. Once melted, add the onion and cook for 4 minutes, stirring occasionally. Add the garlic and cook for 45 seconds, stirring the whole time.
Add the smashed chickpeas and 3 tablespoons Frank’s Red Hot Buffalo Wing sauce. Cook for 2-3 minutes, stirring occasionally until heated through.
Remove pan from heat and set aside.
Toss the shredded mozzarella and cheddar cheeses together to combine them.
Lay a tortilla on a cutting board and sprinkle half with ½ cup shredded cheese. Top with half of the buffalo chickpea mixture. Finish by sprinkling with another ½ cup shredded cheese.
Fold the naked half of the tortilla over the top of the side with fillings. Repeat the step above with the second quesadilla.
Heat a large pan or griddle to medium heat. When warmed up, spritz the surface with cooking spray. Add quesadillas and cook for 5-7 minutes on each side, or until crisp and toasty looking (you may need to cook one at a time, depending on the size of your cooking surface).
Remove from heat and cut into four slices. Serve with ranch dressing or blue cheese dressing.