In a large pan, melt one tablespoon of butter over medium heat. Add the garlic and peppers and cook them in the butter until they’ve softened, about 10 minutes.

Add 2 tablespoons of butter and, once it’s melted, sprinkle the flour over the top of the peppers and garlic. Stir and cook the flour for a minute or so. It will create a thick paste that coats the veggies.

Add chicken broth and stir until there are no clumps of flour. Using an immersion blender (see note), puree the mixture until smooth. Bring the mixture to a simmer. Add the milk and stir. Keep the sauce at a low simmer (don’t let it boil) and stir until it’s thickened. You know it’s ready when you can run the spatula or spoon across the bottom of the pan and catch a glimpse of the pan before the sauce runs back over it. Add the chopped cilantro and salt, stir, and turn off the burner.

Preheat the oven to 375°F. While the oven is preheating, assemble the enchiladas. Coat the bottom of a 9×13″ baking dish with a light layer of sauce. Place some shredded chicken on a tortilla, roll it up and place it in the baking dish. Repeat with the rest of the tortillas and chicken.

Pour the sauce over the top of the tortillas in the baking dish. Sprinkle the shredded cheese in an even layer on top.

Bake the enchiladas, uncovered, for 15 to 20 minutes or until the cheese has melted and the sauce is bubbling. Squeeze lime juice over the top of the enchiladas and garnish with cilantro before serving.