Preheat oven to 375F (190C). Lightly oil a baking dish. Slice the base off each onion, retaining the root, to make a flat surface so the onions stand upright. Make a small slit in the top of each onion and insert some basil and rosemary into each one. Arrange the onions in prepared baking dish.
Whisk together the oil, rice syrup, vinegars, water and salt and pepper to taste. Pour mixture over the onions and bake, uncovered, basting occasionally, until the onions are soft when pierced with a knife, 1 to 1½ hours. Before serving, split the skins and remove; they should pull away very easily. Transfer onions to a platter and serve hot.