Preheat oven to 375°F (190°C). Heat 1 tbsp olive oil in a skillet over medium-high heat. Sear chicken breasts until golden brown, about 4 minutes per side. Remove and let rest.
In the same skillet, add remaining olive oil, onion, and bell pepper. Sauté until onion is translucent and bell pepper softens, releasing a sweet aroma.
Add chili powder and cumin to the skillet, stirring until spices are fragrant, about 1 minute. This step enhances the depth of flavor.
Shred the rested chicken using two forks. Combine with sautéed vegetables in a bowl, adding salt and pepper to taste.
Warm tortillas in a dry skillet for 30 seconds each side, making them pliable and less likely to crack when rolled.
Spread 1/2 cup of enchilada sauce on the bottom of a baking dish. Fill each tortilla with chicken mixture, roll tightly, and place seam-side down in the dish.
Pour remaining enchilada sauce over the filled tortillas, ensuring even coverage. Sprinkle cheddar and Monterey Jack cheeses on top.
Bake in the preheated oven for 15-20 minutes, until cheese is bubbly and lightly browned. Let cool slightly before serving.