1. Heat oven to 425°F. Heat 1/2 tablespoon oil in large nonstick skillet over Medium-High; brown pork on all sides, about 6 minutes.
2. Meanwhile, place onions on aluminum foil-lined baking sheet; drizzle with remaining 1 tablespoon oil and toss to coat. Spread in a thin layer.
3. Place browned tenderloin on top of onions; roast 20 to 25 minutes until internal temperature of pork reaches 145°F to 160°F. Place pork on cutting board; let stand 5 minutes before slicing.
4. Meanwhile, stir cherries, sugar, vinegar, and pepper flakes into onions on baking sheet, fold up and seal edges of foil; let stand while pork is resting to allow flavors to blend. Serve pork and onion-cherry chutney sprinkled with rosemary.