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