Sprinkle pork chops with salt. Place flour in a shallow bowl and dredge chops on both sides.
Warm 2 Tbsp. oil in a large skillet over medium-high heat. Cook chops until browned, 3 to 4 minutes on each side. Transfer to a plate and loosely cover with foil to keep warm.
Add remaining 1 Tbsp. oil, shallot and apples to skillet. Cook, stirring, until softened, 2 to 3 minutes. Add jam, vinegar and broth; cook, stirring and scraping up any browned bits on bottom of skillet, until sauce has thickened, 1 to 2 minutes. Season sauce with salt, pour over chops and serve.
