1. Prepare the Buffalo Chicken Filling: In a medium-sized mixing bowl, combine the shredded cooked chicken, softened cream cheese, Buffalo wing sauce, shredded cheddar cheese, and crumbled blue cheese (if using). Use a spoon or your hands to mix everything together thoroughly until all ingredients are well incorporated and the chicken is evenly coated. The mixture should be creamy and spreadable.

2. Heat the Skillet: Place a large non-stick skillet or griddle over medium heat. Add about 1 teaspoon of butter or a drizzle of olive oil to the pan and let it melt or heat up until shimmering.

3. Assemble the First Quesadilla: Lay one flour tortilla flat on a clean surface. Spread about 1/2 cup of the Buffalo chicken mixture evenly over one half of the tortilla, leaving a small border around the edge.

4. Cook the Quesadilla: Carefully place the tortilla, filling-side up, into the hot skillet. Allow it to cook for about 2-3 minutes, or until the bottom is golden brown and crispy, and the cheese inside starts to melt.

5. Fold and Finish Cooking: Once the bottom is golden, use a spatula to fold the empty half of the tortilla over the filling. Press down gently with the spatula to help the quesadilla crisp up and the cheese melt further. Cook for another 1-2 minutes on this side, then flip and cook for an additional 1-2 minutes on the other side until both sides are golden brown and the filling is hot and gooey.

6. Remove and Slice: Carefully remove the cooked quesadilla from the skillet and place it on a cutting board. Let it rest for a minute before slicing it into wedges using a pizza cutter or a sharp knife.

7. Repeat for Remaining Quesadillas: Add more butter or oil to the skillet as needed and repeat the process with the remaining tortillas and filling until all quesadillas are cooked. Serve immediately while warm.