Rub the pork with the chili powder, cumin, and 1 1/4 teaspoons of the salt. In a large skillet, over medium-high heat, heat 1 tablespoon of the olive oil. Add the pork and brown on all sides. Transfer the pork to a roasting pan; set aside.
In the same skillet, over medium heat, add the remaining olive oil. Add the apples, red onion, garlic, and vinegar and cook 5 to 8 minutes or until the apples and onion are translucent. Add the broth, chilies, jalapeño, sugar, black pepper, cilantro, and the remaining 1/4 teaspoon of salt. Stir and cook, uncovered, over medium-low heat until the apples are tender, 20 to 30 minutes. Add the red pepper during the last 5 minutes of cooking; set aside.
While the salsa cooks, roast the pork for 20 to 25 minutes. Let stand 5 minutes before slicing. Serve with the salsa, buttered potatoes, and a leaf salad.