Scoop out some of the flesh in the center of each avocado; place into mixing bowl. Add cream cheese, tomatoes, salt, pepper, garlic, and cayenne pepper; mix well to combine. Stir in shredded chicken breast.
Scoop spoonfuls of chicken mixture into the each avocado; top each with generous amount of cheddar and Parmesan cheese. Place avocado halves, face-up, in muffin cups to stabilize.
Bake avocados in preheated oven until cheese is melted, 13-15 minutes.
