Preheat oven to 450 degrees F. Put carrots and shallots in a 13x9x2 baking dish.
Meanwhile, melt 2 Tbsp. butter in large skillet until lightly browned. Add sugar, molasses and vinegar. Bring to a boil, stirring constantly until reduced to 1/2 cup (about 2 minutes). Pour mixture over carrots; toss.
Roast, 50 minutes, stirring once, until carrots are tender. Stir in remaining 1 Tbsp. butter and salt. Can be made ahead. Cover and refrigerate overnight. Let stand at room temp for 1 hr., then microwave, covered, on high 5-6 minutes, stirring once.