How to Make It
In a small heavy saucepan, cook the butter and flour over medium high heat, whisking, 1 minute. Pour in the milk and 1/4 teaspoon each salt and pepper and bring to a boil, whisking constantly. Boil 5 minutes, then remove from the heat and whisk in the queso freso. Season the sauce with salt and pepper to taste. Reserve the béchamel.
In a large heavy skillet, heat the oil over medium high heat until hot, then stir in the on-ion, garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper and cook, stirring occasionally, until golden, about 6 minutes. Stir in the chicken and chiles along with their juices, and cook until the chicken is cooked and the liquid is evaporates, about 5 minutes. Season the filling with salt and pepper to taste.
Preheat the oven to 350°F. Divide the filling between the tortillas. Roll each tortilla into a cylinder and place, side-by-side in a baking dish. Pour the béchamel over the tortillas and sprinkle with the cheddar cheese.
Bake the enchiladas until the filling is hot and the cheese is melted, about 10 minutes. Serve.