Preheat an oven to 350 degrees F, or a grill to high (if you are outside, prepare a campfire). Cut any large carrots in half lengthwise and crosswise.
Drizzle a large sheet of foil with some oil. Arrange the carrots in a flat, single layer over half the sheet of foil. Drizzle the carrots with more oil and sprinkle with the garlic, cumin and salt and pepper. Top the carrots with the butter and drizzle with the honey. Fold the foil in half over the carrots and fold the edges to seal and form a pouch. To avoid crowding the carrots, make two pouches if necessary.
Cook the pouch in the oven or on a grill or campfire for 15 minutes. To serve, cut open the pouch tableside and finish with a sprinkle of parsley.