To make the chicken mixture: Heat oil in a medium skillet over medium-high heat. Add shredded chicken, onion, and green chile peppers; cook and stir until heated through and lightly browned. Stir in taco seasoning and prepare according to package directions.

To make the cheese mixture: Combine sour cream, cottage cheese, salt, and pepper in a medium bowl; mix until well blended.

Preheat the oven to 350 degrees F (175 degrees C).

To assemble the enchiladas: Warm tortillas until soft and pliable. Spoon some of the chicken mixture and cheese mixture down the center of each tortilla, then sprinkle with a little Monterey Jack cheese. Roll up and place seam-side down in a lightly greased 9x13-inch baking dish. Spoon any remaining chicken and cheese mixtures over the enchiladas. Pour enchilada sauce evenly over the top, then sprinkle with remaining Monterey Jack cheese.

Bake in the preheated oven until cheese is melted and bubbly, about 30 minutes.