Preheat oven to 400°F and line a rimmed baking sheet with parchment paper; set aside.
Arrange butternut squash halves, cut sides up, and onion quarters on baking sheet. Drizzle with 1 tablespoon oil, rubbing the oil in to cover the cut sides; season with salt and pepper. Flip squash halves over so they are cut side down.
Place garlic clove on square of foil and drizzle with remaining oil. Bring sides of foil up and close tightly to make a packet. Set packet on baking sheet with squash and onion. Roast vegetables for 45 minutes or until squash is tender.
Once the squash is cool enough to handle, carefully scoop the squash flesh away from the skin and into the blender. Squeeze roasted garlic into blender. Add onions, white beans, and broth to blender. Process until very smooth.
Pour contents of blender into large saucepan. Stir in smoked paprika; taste and season with additional salt and pepper, if desired. Heat soup over medium heat until heated through, then stir in apple cider vinegar.
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Notes
If desired, use a handheld immersion blender instead of a blender. Process the soup in the saucepan. The soup will have a slightly less creamy texture.