Pat the beef brisket dry with paper towels and place it on a large cutting board or tray so it is ready to season.
In a small bowl, combine the kosher salt, freshly ground black pepper, ground cumin, chili powder, smoked paprika, dried oregano, garlic powder, onion powder, and brown sugar, stirring until evenly mixed into a spice rub.
Rub the spice mixture all over the beef brisket, pressing it into the surface so it forms a generous, even coating on every side.
Heat the olive oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat until the oil is shimmering.
Add the seasoned brisket to the hot pot and sear it for 3 to 4 minutes per side, turning with tongs, until all sides are deeply browned, then transfer the brisket to a plate.
Reduce the heat to medium, add the sliced yellow onion to the same pot, and cook, stirring often, for about 4 to 5 minutes until the onion softens and begins to brown, scraping up any browned bits from the bottom.
Stir in the minced garlic and cook for 30 seconds to 1 minute, just until fragrant, being careful not to let it burn.
Pour the beef broth and tomato sauce into the pot, stirring well to combine with the onions and garlic and to release any remaining browned bits from the bottom of the pot.
Add the seared brisket back into the pot, nestling it into the liquid and onions, and bring the mixture just up to a gentle simmer.
Cover the pot with a tight-fitting lid, reduce the heat to low, and cook the brisket at a gentle simmer for about 3 to 3.5 hours, turning the meat once or twice during cooking, until it is very tender and easily pulls apart with a fork.
When the brisket is tender, turn off the heat and carefully transfer the meat to a cutting board, letting it rest for about 10 minutes so the juices redistribute.
While the brisket rests, skim any excess fat from the surface of the cooking liquid in the pot, then stir in the freshly squeezed lime juice to brighten the flavor.
Using two forks, shred the rested brisket into bite-sized pieces, discarding any large pieces of fat, and return the shredded meat to the pot with the warm cooking liquid.
Gently stir the shredded brisket into the liquid so it is evenly coated and juicy, then taste and adjust seasoning with a little more salt or pepper if desired.
To warm the tortillas, heat the vegetable oil in a large skillet over medium heat, then add the corn tortillas one or two at a time, warming each side for about 20 to 30 seconds until pliable and lightly toasted, stacking them on a plate and covering with a clean towel to keep warm.
Assemble the brisket tacos by placing a generous spoonful of shredded brisket onto each warm corn tortilla.
Top the meat in each tortilla with shredded cheddar cheese, shredded lettuce, diced tomatoes, chopped fresh cilantro, and diced red onion, dividing the toppings evenly among the tacos.
Finish each taco with a small dollop of sour cream on top, then serve the brisket tacos immediately while warm and tender.