Preheat the Oven: Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Prepare the Filling: In a bowl, mix shredded chicken, Monterey Jack and cheddar cheeses, salsa, green chilies, cumin, chili powder, garlic powder, cayenne pepper, and salt and pepper.
Assemble the Chimichangas: Place a tortilla on a flat surface, add a generous scoop of the filling, fold the sides over, and roll it up tightly, sealing the seam underneath.
Arrange on Baking Sheet: Place the rolled chimichangas seam-side down on the baking sheet. Leave a little space between each one.
Bake to Perfection: Spray the chimichangas with cooking spray. Bake for 20-25 minutes, flipping halfway, until golden brown and crispy.
Serve: Let the chimichangas cool for a few minutes. Serve with sour cream, guacamole, and salsa for dipping.