The roasted acorn squash tastes fabulous when scooped up with spoonfuls of the beet soup. But if oven space is limited, simply serve the soup in bowls.
03Roast squash in upper and lower thirds of oven, switching position of pans halfway through baking, until flesh of squash is just tender, about 1 1/4hours total.
04Cook onion in oil in a 5-quart heavy saucepan over moderate heat, stirring occasionally, until softened. Add beets and apple and cook, stirring occasionally, 5 minutes. Add garlic and cook, stirring, 30 seconds.
05Add broth and 4 cups water, then simmer, uncovered, until beets are tender, about 40 minutes. Stir in vinegar and brown sugar.
06Purée soup in 3 batches in a blender until very smooth, at least 1 minute per batch (use caution when blending hot liquids), transferring to a large bowl. Return soup to pan, then season with salt and pepper and reheat. If soup is too thick, add enough water to thin to desired consistency.