First, prepare your chicken. If you are using pre-shredded chicken, set the chicken aside. If you are baking your chicken or preparing it in the Instant Pot, do that now. When the chicken is shredded, place it into a large bowl and set aside.
Next, create a roux. Heat a medium saucepan over medium/high heat and add butter. Once melted, add the flour to the butter and whisk the two ingredients together. Cook the roux over heat for 1-2 minutes
Slowly add the milk to the saucepan, whisking constantly. Whisk until the cheese sauce has thickened.
Remove the sauce from the heat and add the pepper jack cheese to the saucepan and whisk the cheese into the sauce until melted. Add the cumin and ½ teaspoon of salt to the sauce and whisk to combine.
Pour the pepper jack cheese sauce over the shredded chicken and toss.
Next, heat a large skillet over medium/high heat and add one tablespoon of olive oil to the skillet. When the oil is fragrant, add the onion to the skillet and sauté for 2 minutes. Add the sliced peppers and salsa to the skillet and season with the rest of the salt. Toss the ingredients together and sauté for 3-4 minutes or until the peppers are cooked but not mushy. Remove from heat and add the peppers to a mixing bowl.
Carefully wipe the skillet out with a paper towel and heat the skillet again over medium heat and add 1-2 teaspoons of oil to the pan. Place one tortilla in a skillet and add ¼ cup of shredded monterey jack cheese to the bottom of half of the tortilla. Place ⅓ cup of shredded chicken on top of the cheese, and then ¼ cup of peppers and onions over the chicken. Fold the other half of the quesadilla over all of the ingredients and press the quesadilla down with a spatula. Cook the quesadilla for 3-4 minutes or until the quesadilla is browned. Carefully flip the quesadilla over to the other side and cook for another 3-4 minutes or until brown.
Repeat step 7 until all of the quesadillas are made.
Top your quesadillas with your favorite fixings.