Place butternut squash, cut side down, in a baking dish. Pour water to depth of 1/2 inch. Bake at 375° for 45 minutes or until very tender. Scoop out pulp; set aside.
Heat oil in a large skillet over medium heat. Add onion; cook 30 minutes or until golden brown, stirring frequently. Stir in wine and chicken broth. Bring to a boil; cover, reduce heat, and simmer 10 minutes or until onion is tender. Cool 5 minutes.
Place half of onion mixture and half of squash in a blender; process at low speed until smooth. Return soup to pan; repeat procedure with remaining squash and onion. Bring to a boil; reduce heat, and simmer, uncovered, 5 minutes or until thoroughly heated. Ladle into bowls; spoon 1 teaspoon pesto into center of each bowl. Swirl soup and pesto together using the tip of a knife.