Melt butter in heavy very large skillet over medium-high heat. Add onions; sauté until just tender, about 6 minutes. Add minced thyme, reduce heat to medium and cook until onions are golden, stirring often, about 25 minutes. Add garlic and sauté 2 minutes. Add 1/4 cup wine; stir until almost all liquid evaporates, about 2 minutes. Sprinkle sugar over onions and sauté until soft and brown, about 10 minutes. Add remaining 1/4 cup wine; stir just until liquid evaporates, about 2 minutes. Season to taste with salt and pepper. Cool. (Can be prepare 2 days ahead. Cover and refrigerate.)
Preheat oven to 350°F. Unwrap Brie, reserving bottom of wooden box. Cut away only top rind of cheese, leaving rind on sides and bottom intact. Return Brie to box, rind side down. Place box on baking sheet. Top Brie evenly with onion mixture. Bake until cheese just melts, about 30 minutes. Transfer Brie in box to platter. Surround with baguette slices.