I start by melting butter in a saucepan over medium heat until it’s bubbly. Then I stir in the flour, making a roux, and whisk in chicken broth gradually until smooth. Next, I add minced garlic, diced green chiles, cumin, oregano, salt and pepper. I let it simmer gently until it thickens into a creamy sauce—this becomes what will smother the burritos.
While the sauce simmers, I heat a skillet over medium-high heat and sauté onion until translucent. Then I add the ground meat and cook until browned, breaking it apart. I season with salt and pepper. I stir in the refried beans and half of the shredded cheese so everything binds together. This becomes the hearty filling inside the tortillas.
I warm the flour tortillas briefly (in a microwave or skillet) so they’re pliable. Then I spoon a generous portion of the filling into each tortilla and roll it up tightly, folding in the sides so nothing spills. I place the burritos seam-side down in a baking dish or skillet.
Once all burritos are rolled and arranged, I ladle the green chile sauce over them, making sure they’re well coated. I then sprinkle the remaining cheese over the top. Into a preheated oven they go—baking until the cheese is melted, bubbly, and lightly golden. Finally, I let them rest for a few minutes before digging in.