Smothered Pueblo Green Chile Breakfast Burritos

Method

1. For the sauce, heat the oil in a 3-quart saucepan over medium. Cook half of the onion for 4 minutes until soft, add the garlic for 30 seconds, then stir in the flour and cook 2 minutes, until pale blond and nutty-smelling.
2. Whisk in the broth slowly, then add the chiles, cumin, oregano and ½ tsp of the salt. Simmer over medium-low for 20 minutes, stirring occasionally, until it coats a spoon like a loose gravy. Stir in the lime juice and keep warm.
3. Meanwhile, brown the chorizo in a 12-inch skillet over medium-high for 5 to 6 minutes, breaking it up, until cooked through (160°F). Lift it out with a slotted spoon, leaving the fat behind.
4. Add the potatoes, remaining onion and ¼ tsp salt to the chorizo fat and cook, stirring every 2 minutes, for 10 to 12 minutes until browned and tender. Return the chorizo and scrape everything into a bowl.
5. Wipe out the skillet, melt the butter over medium-low and stir the eggs with the remaining ¼ tsp salt slowly for 4 minutes, until no liquid egg remains but the curds are still soft.
6. Warm the tortillas for 20 seconds in the microwave under a damp towel, then fill each with the potato mixture, eggs and 2 tbsp of the cheddar, folding in the sides and rolling tight. Set the burritos seam-side down in a broiler-safe metal or ceramic 9x13-inch baking dish.
7. Heat the broiler to high with a rack 6 inches from the element. Ladle the green chile over the burritos, scatter on the remaining cheddar and broil for 2 to 3 minutes, until the cheese bubbles and spots brown. Top with cilantro.