Pat the beef brisket dry with paper towels and trim away any large, thick pieces of surface fat, leaving a thin layer for flavor.
Season the brisket on all sides with the kosher salt and freshly ground black pepper, pressing the seasoning gently into the meat.
Heat the vegetable oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat until shimmering.
Sear the seasoned brisket in the hot oil for about 4 to 5 minutes per side, turning as needed, until all sides are deeply browned; transfer the brisket to a plate and set aside.
Reduce the heat to medium and add the sliced yellow onion to the same pot, cooking and stirring for 5 to 6 minutes until softened and lightly golden, scraping up any browned bits from the bottom.
Stir in the minced garlic and cook for 30 seconds to 1 minute, just until fragrant, taking care not to let it burn.
Sprinkle the chili powder, ground cumin, smoked paprika, dried oregano, and ground coriander over the onions and garlic, stirring for about 1 minute to toast the spices gently.
Add the amber beer to the pot, stirring well to deglaze and dissolve the browned bits from the bottom into the liquid.
Stir in the beef broth and tomato paste until the tomato paste is fully incorporated and the liquid is evenly combined.
Return the browned brisket and any accumulated juices to the pot, nestling it into the liquid so it is mostly submerged.
Bring the liquid to a gentle simmer over medium heat, then reduce the heat to low, cover the pot with a tight-fitting lid, and cook for about 3 to 3.5 hours, turning the brisket once or twice during cooking, until the meat is very tender and easily shreds with a fork.
When the brisket is tender, carefully transfer it to a large cutting board and let it rest for about 10 minutes to allow the juices to redistribute.
While the brisket rests, increase the heat under the pot to medium-high and simmer the braising liquid for 8 to 10 minutes, stirring occasionally, until it slightly thickens and reduces in volume.
Shred the rested brisket into bite-sized pieces using two forks, discarding any large pieces of fat, and return the shredded meat to the pot with the reduced sauce.
Stir the lime juice into the shredded brisket and sauce, tasting and adjusting seasoning with additional salt and pepper if desired.
Warm the corn tortillas in a dry skillet over medium heat for about 30 seconds per side, or until soft and pliable, stacking them in a clean kitchen towel to keep warm.
To assemble the tacos, place a small handful of shredded green cabbage down the center of each warm tortilla.
Top the cabbage with a generous spoonful of the beer braised brisket, allowing some of the flavorful sauce to soak into the tortilla.
Sprinkle the diced fresh tomatoes, chopped fresh cilantro, and crumbled queso fresco over the brisket in each tortilla.
Serve the beer braised brisket tacos immediately with lime wedges on the side for squeezing over the top just before eating.