In a medium skillet, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the shredded chicken, cumin, chili powder, and half of the enchilada sauce. Season with salt and pepper, mixing well to combine. Remove from heat.
In a separate bowl, mix the Pepper Jack cheese and half of the cheddar cheese.
Take a flour tortilla and spoon about 1/4 cup of the chicken mixture into the center. Sprinkle with a tablespoon of the cheese mixture, then roll it up tightly and place it seam-side down in a greased 9x13 inch baking dish. Repeat until all tortillas are filled.
Pour the remaining enchilada sauce evenly over the top of the rolled enchiladas. Sprinkle the remaining cheddar cheese on top.
Cover the baking dish with foil and bake for 20 minutes. After 20 minutes, remove the foil and bake for an additional 10 minutes, or until the cheese is bubbly and slightly golden.
Once cooked, remove from oven and let it sit for a few minutes before serving.