Place carrots in a medium saucepan; cover with water. Place over high heat; bring to a boil. Reduce heat; simmer uncovered 6–7 minutes or until tender.
Heat a large nonstick skillet coated with cooking spray over medium heat until hot. Meanwhile, sprinkle salt and freshly ground black pepper, both to taste, over pork chops. Add chops to preheated skillet, and cook them 4 minutes per side, or until barely pink in the center. Combine preserves and ginger; add to skillet with chops. Cook until preserves are bubbly and hot, turning chops once to coat with glaze.
Reserve 2 tablespoons of the carrot cooking liquid. Drain carrots; return to same saucepan and toss with honey mustard. Add reserved cooking liquid and mix well; season with salt and freshly ground black pepper, both to taste. Serve carrots alongside chops.