Trim the excess fat from the pork and cut the pork into 1-inch chunks. Season all over with kosher salt.
Heat the oil in a large, deep skillet or Dutch oven over medium high. Add half of the pork and cook until the pork is browned on all sides, about 4 to 5 minutes (it does not need to cook all the way through). Transfer to a 6-quart or larger slow cooker. Repeat with the second half of the pork.
Pour in the chicken broth and with a wooden spoon or sturdy spatula, scrape any browned bits off of the bottom of the pan. Let most of the liquid cook off, then add the carrots and onions. Saute until the vegetables begin to brown, about 4 minutes.
Stir in the garlic, chili powder, cumin, and oregano. Cook just until very fragrant, about 30 seconds. Add to the slow cooker with the pork.
To the slow cooker, add the salsa verde, enchilada sauce, and green chiles. Stir to combine.
Cover and cook on low for 3 to 4 hours, until the pork is tender and cooked through (pork loin is leaner than pork shoulder, so it cooks much more quickly than other slow cooker pork recipes).
Stir the ingredients together to recombine, then taste and adjust seasoning as desired. Ladle into bowls and serve hot with warm tortillas and toppings of choice.
TO STORE: Refrigerate leftovers in an airtight storage container for up to 3 days.
TO REHEAT: Gently rewarm pork in a Dutch oven on the stovetop over medium-low heat or in the microwave.
TO FREEZE: Freeze leftovers in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.