Step 1

Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish.

Step 2

Heat 2 tablespoons of oil in a skillet over medium-high heat. Fry tortillas (1 at a time) for 5 seconds on each side to soften and make them pliable. Add more oil to pan as needed. Drain between layers of paper towel and keep warm.

Step 3

Divide chicken, 10 ounces of Monterey Jack cheese, and onion among the 12 tortillas. Roll up each tortilla and place seam-side down in the prepared pan.

Step 4

Melt butter in a saucepan over medium heat. Add flour and whisk until mixture begins to boil. Slowly add broth, stirring with a whisk until thickened. Mix in the sour cream and chiles, heating thoroughly but do not boil, stirring occasionally. Pour mixture over the enchiladas.

Step 5

Bake in the preheated oven until bubbly and heated through, about 20 minutes. Top with remaining Monterey Jack cheese and bake for 5 more minutes. Garnish with chopped green onions and cilantro.