Preheat the oven to 400 degrees.

Mix together the mozzarella and cheddar cheeses, and form them into a large circle shape on a parchment-lined baking sheet.

Bake the cheese for 10 minutes until starting to brown on the edges, and it has taken on a lacelike appearance.

In a skillet over medium heat on the stove, heat the olive oil.

Add the red onions to the skillet, and cook until just starting to soften.

Place the shredded chicken in the skillet, and add the hot sauce. Toss to coat.

Mix in salt and pepper to taste.

Remove the cheese from the oven, and let sit for a minute or two.

Place the chicken mixture in an even layer on one half of the cheese circle.

Fold the other half of the cheese circle over the top of the filling, and bake for an additional 3-5 minutes.

Let sit to cool for several minutes before serving.