Heat Dutch oven or stock pot to medium. Add 2 tablespoons of cooking oil and braise the roast on all sides. Remove the roast from the pan and set aside.
Increase heat to medium-high. Add 2 tablespoons of oil and sauté the onion. Once the onions are translucent, add 6 tablespoons of Birria Blend and beef broth. Stir to combine, and then place the roast back in the pot.
Reduce heat low and simmer for 3-4 hours, until meat is fall-apart tender. Skim fat off the top of the broth and reserve for making birria tacos.
Remove meat and shred the beef with two forks or meat shredders. Add tomato paste to birria broth and stir to combine. Then put the shredded meat back in birria broth.
Dip corn tortillas in the reserved beef fat and heat in a skillet or on a flattop on medium heat. Add about 3 tablespoons of the shredded birria meat inside the tortilla and fold in half onto itself. Crisp the tortillas until golden brown and crispy, about 10 minutes.
Serve the birria tacos with crumbled cheese, diced white onion, chopped cilantro, lime wedges, and a side of the birria broth for dipping.
