Pat the beef brisket dry with paper towels and trim any large, excess pieces of surface fat, leaving a thin layer for flavor.
In a small bowl, combine the kosher salt, black pepper, chili powder, ground cumin, smoked paprika, and dried oregano, stirring until evenly mixed.
Rub the spice mixture all over the brisket, coating both sides and pressing gently so the seasonings adhere well to the meat.
Heat the olive oil in a large skillet over medium-high heat until shimmering, then add the brisket and sear for 3 to 4 minutes per side, until nicely browned; transfer the seared brisket to the slow cooker.
Add the sliced yellow onion and minced garlic to the same skillet and cook over medium heat for 2 to 3 minutes, stirring, until the onion begins to soften and picks up some of the browned bits from the pan.
Pour the beef broth and tomato sauce into the skillet with the onions and garlic, stirring and scraping the bottom to deglaze and combine everything into a flavorful cooking liquid.
Pour the broth and tomato mixture evenly over the brisket in the slow cooker, making sure the onions and garlic are distributed around the meat.
Cover the slow cooker with its lid and cook the brisket on LOW for 8 hours, or until the meat is very tender and easily shreds with a fork.
Carefully transfer the cooked brisket to a large cutting board or shallow dish, then use two forks to shred the meat into bite-sized pieces, discarding any large pieces of fat.
Skim any excess fat from the surface of the cooking liquid in the slow cooker, then return the shredded brisket to the slow cooker and stir to coat the meat in the sauce.
Stir the lime juice and chopped fresh cilantro into the saucy shredded brisket, tasting and adjusting seasoning with a pinch of additional salt or pepper if desired.
Warm the corn or flour tortillas in a dry skillet, in the microwave, or wrapped in foil in a low oven until soft and pliable.
To assemble the brisket tacos, place a generous spoonful of the shredded brisket onto each warm tortilla.
Top each taco with shredded lettuce, diced tomatoes, diced red onion, shredded cheese, and a small dollop of sour cream.
Serve the brisket tacos immediately while warm, allowing everyone to add more toppings as desired.