1. Trim excess fat from pork. Place a 10- to 12-inch nonstick frying pan over medium-high heat. When pan is hot, add oil and chops. Cook until browned on both sides, about 5 minutes total.
2. Add orange juice, salsa, sugar, cumin, and ginger. Bring to a boil, then reduce heat to low; cover and simmer until pork is tender when pierced, 40 to 45 minutes. Skim off fat; discard. Transfer pork to a serving dish and keep warm. Boil sauce, uncovered, over high heat until reduced to about 1 cup, about 4 minutes. Add salt to taste. Garnish with cilantro and orange slices.