Sprinkle kosher salt and 1 teaspoon black pepper over the fatty side of brisket. Spread tomato paste over entire brisket. Place brisket, fat-side up, in a heavy pot; pour in enough water to cover brisket. Add halved onion, carrot, celery, 1/2 of the cilantro, and garlic to the pot. Bring liquid to a boil. Cover pot with a lid or aluminum foil and transfer to oven.
Bake in the preheated oven until brisket is very tender, about 6 hours.
Blend chipotle peppers in adobo sauce in a a food processor until finely chopped. Add vinegar to peppers and continue processing; drizzle olive oil into mixture until smooth.
Remove brisket from liquid and cool slightly. Slice meat across the grain into 2-inch slices; shred thoroughly with a fork.
Combine shredded meat, chopped onion, tomato, remaining cilantro, and pepper mixture in a large bowl; season with salt and pepper. Serve meat mixture with corn tortillas and top meat with Monterey Jack cheese.