Heat a tablespoon or so of olive oil into a large skillet over medium-high heat then carefully swipe it with a paper towel so it evenly coats the entire skillet surface. Fry the tortillas one at a time for a few seconds on both sides just until they start to crisp and get a little color.
In the same skillet add another drizzle of olive oil and the onion and bell pepper. Season it with ½ tsp cumin, salt and pepper to taste, sautéing a few minutes until the vegetables are tender.
Fold in the carnitas or chicken, half of the can of green chilies, 1 ¼ cup of Monterey jack cheese and 2 tablespoons of cilantro. Use a spatula and score the filling into six equal sections.
Begin assembling the tortillas, dividing the meat mixture between the tortillas then roll and set aside.
Wipe the same skillet with a damp paper towel then add the Salsa Verde, remaining green chilies, cream cheese, other 1/2 teaspoon of cumin and the remaining cilantro. Simmer over medium low heat until it’s completely blended. Temper the sour cream then add it to the sauce, combining.
Spread 2 tablespoons of sauce into the bottom of the baking dish. Gently add the rolled tortillas and pour the sauce over the tortillas.
Scatter the remaining Monterey Jack cheese over the top and bake at 375° for 20-25 minutes or until hot and bubbly.