Remove the seeds from the guajillo chilies.

Peel and chop one white onion.

Cut the top off the garlic bulb and remove some of the outer skin.

Cut the beef into large chunks.

Grind cumin, coriander, peppercorns, cloves, and oregano into a fine powder.

In a large pot, add the beef, guajillo chilies, chopped onion, garlic bulb, bay leaves, ground spice mix, salt, beef broth, and water.

Bring to a boil over high heat and cook for about 30 minutes.

In a blender, add quartered Roma tomatoes.

Remove the guajillo chilies, onion, and garlic from the pot (peel the garlic first), along with about ½ cup of broth.

Blend these with the tomatoes until smooth.

Strain the sauce into the pot and stir to combine.

Reduce the heat to low-medium.

Let the birria simmer for 3 hours, with the lid slightly ajar, stirring every 30 minutes.

Once the beef is very tender, remove it from the pot and let it cool slightly. Shred with two forks.

Skim off the red oil that rises to the top of the broth and set it aside in a small bowl or plate.

Finely chop the remaining onion.

Chop half the cilantro, and keep the rest as whole leaves for garnish.

Shred the cheese and cut the limes into wedges.

Dip each tortilla in the reserved red oil from the broth.

Place on a skillet or griddle over medium heat, add cheese, and top with shredded beef.

Cook for about 1 minute, then fold the tortilla in half.

Cook another minute per side until crispy and golden. Repeat for all tortillas.

In a small bowl, ladle some of the hot birria broth. Stir in chopped onions and cilantro.