Preheat oven to 375°F. Line a baking sheet with parchment paper. Put a large, wide-mouth glass jar in the center of the baking sheet.
Using a cutting board and a sharp knife or a pizza cutter, cut the tortillas in half. Cover the halved tortillas with a clean, dry cloth and set aside.
In a large mixing bowl, combine the shredded cooked chicken, diced yellow pepper, finely diced yellow onion, finely diced red onion, salsa, and taco sauce. Stir well until all of the ingredients are completely incorporated.
Sprinkle 1½ to 2 tablespoons each of the shredded Colby and Monterey jack cheese and the chicken mixture.
Roll each of the halved, filled tortillas into a cone shape. Be careful not to squish out the filling. The small pointed ends of the cones need to touch the wide-mouth jar and form a ring around the jar.
Once you have made a complete bottom layer, about 12 to 13 cones, sprinkle ¾ cup of the shredded cheddar cheese on top of the ring.
Repeat the ring of cones for a second layer. Then top with 1 cup of the Colby and Monterey jack cheese.
Repeat for the third and final ring. Remove the glass jar from the center of the cones.
Bake for 15 to 20 minutes, or until the edges of the cones are golden brown and the cheese is melted.
Using the edges of the parchment paper, carefully transfer the quesadilla ring to a heat-safe serving plate.
Serve the quesadilla ring with your favorite salsa or dipping sauce.
Covering the tortillas will help ensure they remain soft while making your filling.
Oven temperatures vary and may need to be recalibrated periodically to ensure they are accurate. Make sure to check your quesadilla ring at the lower end of the recommended baking time.
If you want to trim the excess parchment paper, be very careful not to touch the hot cheese!