Preheat oven to 400 degrees, with rack in the middle position. Heat oil in a 12-inch, heavy, ovenproof skillet over moderately high heat until very hot and just beginning to smoke, then add half of the carrots, cut sides down. Cook, undisturbed, until they begin to brown, 12 to 15 minutes. Transfer to a plate.
Brown remaining carrots similarly, but leave them in the skillet. Add butter to skillet and return carrots on plate to skillet. Continue to cook over moderately high heat, turning frequently, until carrots are golden brown on the edges, about 5 minutes more.
Add garlic, thyme, sea salt, pepper and water, and cover skillet tightly with a lid. Roast in oven until carrots are tender, about 20 minutes. Remove lid and continue roasting, turning over carrots occasionally, until edges are slightly crisp, 10 to 15 minutes more.