In a large skillet, heat 1 tablespoon oil over high. Season pork with salt and pepper. In three batches, cook pork until browned on all sides, about 15 minutes total (add up to 1 tablespoon oil as needed). Transfer pork to a 6-quart slow cooker.
Add broth to skillet, stirring and scraping up browned bits with a wooden spoon. Pour broth into slow cooker, then add onion, garlic, cumin, carrots, chiles, and potatoes. Cover and cook on high until meat is fork-tender, 6 hours.
Skim excess fat from top of chili. With a slotted spoon, transfer 2 cups chili (leaving liquid behind) to an airtight container; let cool, uncovered, then refrigerate for Thursday (see Pork and Cabbage-Slaw Burritos). Serve remaining chili with cilantro, warmed flour tortillas, and lime wedges.
Preheat oven to 350 degrees. In a large Dutch oven or heavy ovenproof pot, heat 1 tablespoon oil over high. Season and brown pork as per step 1; transfer to a plate. Add onion, garlic, and cumin to pot and cook until onion is soft, 3 minutes. Add broth, pork, and 2 cups water. Cover and cook in oven 1 1/2 hours. Remove from oven and add carrots, chiles, and potatoes. Cover, return to oven, and cook until potatoes are tender and meat is fork-tender, about 45 minutes.
Smart Time-Saver: Set aside extra chili to make burritos later in the week.