Pat the beef brisket dry with paper towels and trim any large, excess pieces of fat, leaving a thin layer for flavor.

In a small bowl, combine the kosher salt, black pepper, ground cumin, chili powder, smoked paprika, garlic powder, onion powder, and dried oregano to make a spice rub.

Rub the spice mixture all over the brisket, pressing it gently into the surface so it adheres well.

Heat the olive oil in a large, heavy pot or Dutch oven over medium-high heat until shimmering.

Sear the brisket for 3 to 4 minutes per side, until each side is nicely browned, then remove the brisket to a plate.

Pour the beef broth and tomato sauce into the pot, scraping up any browned bits from the bottom with a wooden spoon.

Return the brisket and any accumulated juices to the pot, cover with a lid, reduce the heat to low, and simmer gently for about 3 to 3.5 hours, or until the brisket is very tender and can be shredded easily with a fork.

While the brisket cooks, rinse the long-grain white rice under cold water until the water runs mostly clear.

In a medium saucepan, combine the rinsed rice, water, and salt for rice, then bring to a boil over medium-high heat.

Once boiling, reduce the heat to low, cover, and cook for about 15 minutes, or until the rice is tender and the water is absorbed, then remove from heat and let stand covered for 5 minutes before fluffing with a fork.

When the brisket is tender, remove it from the pot to a cutting board and let it rest for about 10 minutes.

Use two forks to shred the brisket into bite-size pieces, discarding any large fatty bits.

Stir the lime juice into the cooking liquid in the pot, then return the shredded brisket to the pot and toss to coat it evenly in the sauce.

Place the drained and rinsed black beans in a small saucepan over low heat and warm gently, stirring occasionally, until heated through.

Warm the flour tortillas in a dry skillet over medium heat for about 30 seconds per side, or until soft and pliable, then stack them on a plate and cover with a clean kitchen towel to keep warm.

To assemble each burrito, lay a warm flour tortilla on a flat surface and add a line of fluffed rice slightly off-center, leaving space at the edges for folding.

Top the rice with a portion of shredded brisket, then add some warmed black beans, shredded cheese, a spoonful of sour cream, a spoonful of salsa, and a sprinkle of chopped fresh cilantro.

Fold the sides of the tortilla over the filling, then fold up the bottom and roll tightly into a burrito, tucking in the filling as you go.

If desired, place the assembled burritos seam-side down in a warm skillet for 1 to 2 minutes per side to lightly toast the tortillas and help seal them.

Serve the brisket burritos warm, with any extra salsa, sour cream, and cilantro on the side if you like.