Make the Broth: Heat oil in a pot over medium heat. Add yellow onions and sauté until translucent. Stir in garlic and cook for 30 seconds until fragrant.
Toast the Spices: Add salt, cloves, red chili powder, cumin, oregano, pasilla powder, cinnamon, and whole peppercorns. Stir for about a minute until aromatic.
Add Tomatoes & Liquid: Pour in San Marzano tomatoes, crushing them with a wooden spoon. Sauté for a few minutes, then add veggie broth, 4 cups of water, dried chiles, and bay leaves.
Simmer & Blend: Let the broth simmer on low-medium heat for about an hour. Add another 1.5 cups of water 20 minutes before it’s done. Remove bay leaves, then blend until smooth using an immersion blender.
Prepare the Mushroom "Meat": Shred the king oyster mushrooms using a fork. Heat oil in a pan, add the mushrooms, and sauté until they release their water. Stir in taco seasoning and cook for another minute. Pour in 1/3 cup of the birria broth and let it fully absorb.
Assemble the Tacos: Heat a pan over medium heat. Dip tortillas in the broth, then place them on the pan. Fill with mushroom "meat" and cheese, then fold the taco in half.
Cook Until Crispy: Press down gently and cook for 2-3 minutes per side until crispy and golden. Add more broth as needed to keep them moist.
Serve: Garnish with yellow onions and cilantro, and serve with extra broth for dipping.