Prepare 8 ½ x 11″ baking dish with nonstick spray.
In a small pan over medium heat, melt butter and add flour. Stir constantly and cook. Add enchiladas sauce, broth, salt, and pepper and stir. Bring to boil; reduce heat and simmer until thickened, about 15 minutes. Keep warm over low heat.
In a large pan, heat oil until shimmering. Add onions and green chiles and cook, stirring, 5 to 7 minutes.
Stir in cumin and chili powder, then add chicken, sour cream, and queso fresco. Stir until creamy, about 4 minutes.
Remove enchilada sauce from heat. Spread 1/2 cup of sauce in bottom of baking dish. Working with 1 tortilla at a time, dip tortillas in remaining enchilada sauce and fill with 1/3 cup of chicken filling. Roll tortilla around filling and place seam-side down in baking dish.
Repeat with remaining tortillas.
Pour remaining sauce over rolled enchiladas and sprinkle with Monterey Jack.
Bake until cheese is fully melted and bubbly, 25 to 30 minutes. Remove from oven and let rest 5 minutes. Garnish with scallions and serve.
For easy shredded chicken, use a rotisserie chicken or poach chicken breasts.