Preheat the oven to 375°F. Line a baking sheet with parchment paper.
In a large bowl, combine the chicken, onion, red bell pepper, jalapeño, and taco sauce. Set aside.
Cut each tortilla in half. Evenly distribute about 2 tablespoons each of cheddar cheese, Monterey Jack cheese, and the chicken mixture onto each tortilla half.
Roll each tortilla half into a cone shape, starting from the cut edge, making sure not to push the ingredients out.
Place a wide-mouth jar or glass in the center of the baking sheet.
Arrange about 13 tortilla cones around the jar to form a ring, with the points of the cones touching the jar in the center. Sprinkle cheddar and Monterey Jack cheese over this layer.
Repeat with the remaining cones to create 2 more layers, finishing with the rest of the cheddar and Monterey Jack cheese.
Remove the jar from the center of the ring.
Bake for 15-20 minutes, until the cheese is melted and the edges of the tortillas are crispy.
Carefully transfer the blooming quesadilla ring to a serving platter. Place your dip of choice inside the ring and top with your desired garnishes.