Toast the ancho and guajillo chiles in a dry Dutch oven over medium heat for 30 seconds per side until fragrant but not blackened.
Soak the chiles in the hot broth for 15 minutes, then blend the chiles and broth until completely smooth.
Heat the oil in the Dutch oven, cook the onion for 6 minutes until golden at the edges, and stir in the garlic, cumin and tomato paste for 1 minute.
Pour in the chile puree, add the brisket and salt, and simmer uncovered for 40 minutes until the meat reaches 165°F and the sauce turns glossy.
Stir in the lime juice and rest the chili for 10 minutes before serving so the sauce settles.