Place the meat in a large pot and cover with at least 12 cups water. Add the white onion half, 5 garlic cloves, bay leaves, salt and black peppercorns. Bring to a rolling boil over high heat. Skim off any foam that rises to the top, reduce the heat to medium-low, cover and cook until the meat is completely cooked through and tender enough to pull apart easily with your fingers, about 1 1/4 to 1 1/2 hours.
Using a slotted spoon, remove the meat from the broth and place in a bowl. Strain the broth into a separate bowl or container. Measure out 4 cups and freeze the rest for another use. Once the meat is cool enough to handle, shred into smaller bite size pieces and remove and discard the fat. Set aside.
To make the carne con chile:
Place the chiles colorados, tomatoes, and 2 garlic cloves in a medium saucepan. Cover with water and bring to a simmer over medium-high heat. Reduce heat slightly and simmer for 10 to 12 minutes until the chiles have plumped up and rehydrated, and the tomatoes are fully cooked and mushy. Transfer the chiles, tomatoes, garlic and a 1/2 cup of their cooking liquid to a blender. Add the chopped white onion, chiltepin chiles, chiles de árbol, oregano and salt. Puree until completely smooth.
Heat the lard or oil in a large heavy-bottomed pot or Dutch oven set over medium-high heat. Add the flour and stir together well to create a roux. Cook, stirring, for a minute or two until bubbling and lightly browned. Add the chile colorado puree. Cook, stirring often, making sure the mixture doesn’t stick and burn on the bottom of the pan, until it has thickened and darkened slightly, about 5 to 6 minutes. Stir in the beef broth and the shredded cooked meat and bring to a simmer, stirring. Reduce heat to medium, cover partially, and continue to cook, stirring often and scraping the bottom of the pot until the sauce has thickened and the meat is well seasoned, coated with the chile mixture, and so tender it is falling apart, about 30 minutes. Taste and adjust salt. Remove from the heat.
To make the burritos:
Heat the tortillas on a preheated comal or skillet. Top with 1/4 to 1/3 cup of the carne con chile and roll into burritos. Once assembled, you can heat them for another minute if you want them a bit toasted, or eat them soft, just as soon as they are assembled.
Serve with sliced or diced avocado, crumbled queso fresco, crema, salsa and lettuce, and let people garnish to taste.