Preheat oven to 475°F Mix oil, garlic, and chopped thyme in small bowl. Rub mixture over pork, shallots, and pears. Heat large nonstick skillet over medium-high heat. Add pork and shallots; brown on all sides, turning, about 7 minutes. Transfer shallots to platter. Transfer pork to baking sheet (do not clean skillet). Roast pork until thermometer inserted into center registers 145°F, about 10 minutes.
Meanwhile, add pears to same skillet and cook over medium-high heat until brown on cut side, turning once or twice, about 4 minutes. Transfer pears to platter (do not clean skillet).
Mix butter and flour in small cup. Add broth, pear nectar, and butter mixture to same skillet; boil until sauce thickens, scraping up browned bits, about 7 minutes.
Slice pork; arrange on platter. Surround with pears and shallots. Drizzle sauce over pork. Garnish with thyme sprigs.