Season both the beef and lamb well on all sides with sea salt and pepper. Set aside.

Next, add the oil to a large pot or rondeau over high heat. Once it begins to smoke add in the meat and lamb and sear until well browned on all sides, about 6-8 minutes per side.

Remove the beef from the pot and set it aside.

Now, place in the onions and cook over medium heat for about 20-25 minutes or until caramelized.

Place in the garlic and give it a quick sauté with the onions for about 4-5 minutes.

Next, pour in the tomatoes, chiles, allspice berries, cinnamon, peppercorns, bay leaves, cumin seeds, oregano, and thyme and stew on medium-high heat for 8-10 minutes to soften up the peppers and cook the tomatoes.

Deglaze with 2 cups of water and continue to cook on medium-high heat until the liquid is reduced by ½ or about 15 minutes.

Transfer the mixture to a blender and puree at high speed until smooth. See note on how to blend hot food.

Pour the mixture back into the pot along with water or beef stock. Season this mixture well with salt and pepper.

Place the seared meat back into the pot, cover, and cook on medium-medium-high for about 2 hours, or until the meat is easily shredded. The liquid should be at a rapid bubble or a very low boil the entire time.

Remove the meat, discard any bones, and roughly chop on a cutting board. Keep aside.

Next, strain the remaining liquid through a fine-mesh strainer or chinois and return it to the pot along with the chopped meat.

To serve: Place the desired amount of birria consomé into a bowl and garnish with fresh-squeezed lemon juice, onions, radishes, and cilantro.