In a large bowl, combine the Oaxaca and cheddar cheese until evenly mixed. Divide the cheese mixture into two equal portions. Set one aside for the refried beans and the other for assembling the burritos.

Heat a large skillet over medium heat. Melt the lard with the olive oil. Add the onion and cook until slightly softened. Stir in the jalapeños and cook until the onions are lightly golden.

Reduce the heat to medium-low. Add the garlic, smoked paprika, ground ancho chile, ground cumin, and oregano. Cook, stirring constantly, for 1 minute, or until fragrant.

Stir in the cooked beans. Gradually add the reserved bean broth while mashing with a potato masher until mostly smooth with some texture remaining.

The amount of broth will vary, so stop adding it once the beans are creamy and spreadable, yet thick enough to hold their shape inside a burrito. Keep in mind they will continue to thicken as they cool.

Once the beans are hot and have reached the desired consistency, stir in 10 ounces of the cheese mixture until melted. Season with salt to taste, then remove from the heat.

Warm the flour tortillas until soft, pliable, and heated through, being careful not to crisp them.

Fold the sides of the tortilla over the filling. Fold the bottom edge up and over the filling, then roll tightly into a burrito. Repeat with the remaining tortillas and filling.