Step 1

Preheat the oven to 350 degrees F (175 degrees C).

Step 2

Heat a large skillet over medium heat. Cook and stir chorizo in the hot skillet until browned and crumbly, 5 to 7 minutes. Add onion and garlic and cook until transparent, 4 to 5 minutes more.

Step 3

Melt butter in saucepan over medium-high heat until sizzling. Stir in flour and whisk until a paste forms, about 5 minutes. Whisk in milk and continue to cook, whisking, until sauce begins to thicken, about 5 more minutes. Stir in the chorizo mixture, shredded cheese, and green chiles. Continue stirring until smooth and thick.

Step 4

Transfer mixture into a shallow baking dish.

Step 5

Bake in the preheated oven until browned, about 25 minutes.