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Preheat oven to 450 degrees.
Toss carrots with olive oil, sea salt, and pepper, spread in single layer on baking sheet, and place in oven. Pat chops dry and season on both sides with sea salt, pepper, and dried rosemary. When carrots have been cooking 10 minutes, add pork chops to same baking sheet in oven. After 4-5 minutes, flip chops. Roast 7-10 minutes total, until cooked through or meat thermometer registers 150 degrees.
While pork is cooking, place cider in sauté pan over medium heat. Reduce by at least half. When carrots are tender, remove from oven and add to sauté pan along with butter. Simmer a few minutes (your pork chops should be out of oven and resting at this point) to absorb cider glaze. Serve chops with glazed carrots.