Add coarsely chopped tomatoes and onions, chiles, bay leaves, peppercorns and a cinnamon stick to a large pot and cover completely with warm water. Bring to a boil, then reduce heat and simmer for 5 minutes. Cover and remove from heat allowing everything to soften. In the meantime, you can start shredding the mushrooms (see step 8 below).
Remove solid ingredients from the pot using a slotted spoon, and transfer them to your blender. Don't throw away the chili water. You'll use some of it in the next step.
Add 1 cup of chili water to the blender, then vinegar, garlic cloves, cumin, oregano, cloves and lime juice. Cover with vegetable broth almost to the top. You may have to work in 2 batches, if your blender is smaller.
Blend on high speed until the mixture is smooth and creamy, about 2-3 minutes.
Strain the sauce (I love this strainer) over a large bowl (optional but recommended). If straining, use a spoon to press down on the solids in the sauce in your strainer to ensure you get every drop of sauce into the bowl.
Once all your mixture is strained in the bowl, set aside.
Using your fingers, shred each mushroom into small, thin pieces. This will take the longest, that's why I suggest starting this step while your sauce is cooking.
Heat olive oil in a large skillet. Add mushrooms and a teaspoon of black pepper. You'll salt them too, but wait until they're almost done so they don't get watery. I fry them on medium-high heat until browned and crispy on all sides.
Add a cup or two of birria broth to the mushrooms, stir and simmer on low heat for 10 minutes.
Before you dip your taco shell into the broth, heat on both sides over an open flame on your stovetop. This will keep them from getting too soggy when you fry them. Either dip the tortilla in the sauce or use a basting brush to spread the consommé over both sides.
Heat a thin layer of vegetable oil in a small skillet. Add a tortilla. open-faced to the skillet, and fry each side for about 1 to 1 1/2 minutes, being careful not to burn it (a few charred marks are ok). If you need to, turn down the heat. Next, add a layer of vegan birria to the taco shell, followed by a layer of cheese and a sprinkle of chopped onion and cilantro.
Using tongs, gently fold your taco over the ingredients and press down to ensure they meld together. Place each taco on a sheet pan or large plate with a layer of paper towels to absorb the excess oil.
Continue frying each taco until all the birria is used up. Divide onto plates and garnish with more chopped onion and cilantro. Finish with a few squirts of lime. Serve immediately with my Cilantro Lime Rice and Cantaloupe Agua Fresca (you'll need it) and a side of consommé for each guest . Enjoy!