In a large mixing bowl, combine 1 cup (125g) all-purpose flour and 1 tablespoon of salt. Add 1 tablespoon of lard and rub it into the flour with your fingertips until the mixture resembles coarse sand. Gradually add warm water, 1 tablespoon at a time, mixing with a fork until a shaggy dough forms.

Turn the dough out onto a lightly floured surface. Knead for 10 minutes or until it doesn't stick to your hands, adding flour as needed. Let rest for 20 minutes.

Divide the rested dough into 2 equal pieces. On a lightly floured surface, shape each piece into a ball, then roll out with a rolling pin into a circle approximately 12 inches / 30cm wide, rotating the dough a quarter turn between each roll to keep it round.

Heat 1 tablespoon of vegetable oil in a 12-inch / 30cm cast-iron skillet over medium heat. Add the chorizo, breaking it up with a spoon, and cook for 5–6 minutes until the fat renders and the chorizo is cooked through. Add the ground beef to the skillet and cook in the chorizo fat for 6–8 minutes, breaking it into small pieces, until it reaches an internal temperature of 160°F / 71°C. Remove from the skillet and set aside.

Remove stems from dried chiles, break them open, and shake out the seeds. Heat 1 tablespoon of lard in a medium saucepan over medium heat. Add the chiles and roast for 30–60 seconds per side, pressing them flat with a spatula, until fragrant and slightly darkened — do not burn them. Add 1 cup of water, bring to a simmer, and cook for 5 minutes until the chiles are softened. Remove the chiles and set aside; discard the soaking water.

In the same saucepan, heat 1 tablespoon of lard over medium heat. Add 1/3 cup of the diced yellow onion with a pinch of salt. Sauté for 3–4 minutes until softened. Add the sliced tomatillos, halved tomatoes, and garlic cloves.

Simmer on low heat for 15–20 minutes until the tomatillos and tomatoes have broken down and the garlic is soft. Transfer the vegetable mixture along with the softened chiles to a blender. Add 1 tablespoon of white vinegar and 1/2 teaspoon of salt. Blend until mostly smooth — a slightly rustic texture is fine.

Put avocado pieces in a blender. Add the cilantro, a little bit of onion, serrano peppers, 1 clove of garlic, lime juice, a little salt, and about 1/2 cup of water. Blend until smooth.

Warm both sides of a rolled tortilla in the cast-iron skillet to make it flexible. Melt some white cheddar and Oaxaca cheese in the skillet.

Place the rolled tortilla directly onto the melted cheese in the skillet. Press gently for 10–15 seconds until the cheese adheres to the tortilla, then carefully lift the tortilla out with a spatula and place it cheese-side up on a clean work surface.

Add chorizo and ground beef to one side of the tortilla; don't overfill. Put tres chiles sauce on the meat, then the avocado sauce, some diced onions, and cilantro.

Fold in left and right sides a little, then tightly roll the burrito, keeping the sides closed. Heat for a minute in the skillet to secure it.