Set each onion on its root end in a baking dish that has been lightly oiled. From top, cut through middle of each onion to 1/2 inch from bottom. Repeat cuts 1/2 to 3/4 inch apart to make 10 or 12 attached wedges on each onion.
Set onions, cuts up, in a glass dish. Drizzle evenly with oil, and then sprinkle lightly with salt and pepper.
Bake, uncovered, in a 375° oven until onions are tender when pierced in center, about 45 minutes.
When fully cooked, spoon balsamic vinegar over the top of each onion: return to the oven for about 10 minutes.