Cut chuck roast into large pieces. Season with salt and pepper.
Heat a Dutch oven over medium heat with olive oil. Add the pieces of Chuck roast, careful not to crowd. Brown all sides. You may need to work in batches. Remove from the pot.
Add the garlic, onion, and tomato paste. Cook for several minutes, allowing the tomato paste to deepen in color.
Add the remaining ingredients, including the browned chuck. Make sure to add any drippings that have accumulated on the plate.
Cover and allow to simmer for 1 hour.
Remove the softened chiles, the onions, and some of the broth and add to a blender or food processor. Blend until smooth and silky. Pour back into the pot.
Allow to simmer for 3 more hours or until the beef is fall apart tender.
Shred the meat and add back to the sauce.
Tacos
To build your Beef Birria Tacos heat a large skillet over medium heat.
Dip a tortilla into the sauce. Add shredded cheese to half of the tortilla along with some of the shredded beef.
Fold the tortilla over and brown both sides.
To serve, top with chopped onions, cilantro, and serve with wedges of lime and cups of the reserved consommé for dipping. Enjoy!