Directions

• Preheat oven to 400°F. Toss sourdough pieces with 3 tablespoons olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper on a rimmed baking sheet. Bake in preheated oven until golden brown, 8 to 10 minutes, stirring occasionally. Transfer croutons to a small bowl; set aside. Wipe baking sheet clean. (Do not turn oven off.)
• Cut off and discard top 1/2 inch of garlic head. Place garlic head, cut side down, and onion wedges on rimmed baking sheet. Drizzle evenly with remaining 3 tablespoons olive oil, and sprinkle with 3/4 teaspoon salt and remaining 1/4 teaspoon pepper. Roast at 400°F until onions and garlic are tender and just starting to brown, 30 to 35 minutes. Pour wine over onions. Continue roasting until liquid is mostly evaporated, about 5 minutes.
• Squeeze softened garlic cloves into a blender using tongs; discard garlic skins. Transfer onions and remaining liquid on pan to blender. Add chicken stock, Parmesan, and remaining 1/2 teaspoon salt. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over lid opening. Process on medium-high speed until smooth, about 2 minutes. Decrease speed to medium-low. With blender running, slowly pour in cream. Add butter, a few pieces at a time, and blend until soup is very smooth and creamy, about 30 seconds. Thin soup to desired consistency with additional chicken broth, if desired. Season to taste with additional salt.
• Divide soup among serving bowls. Top with croutons; drizzle with additional olive oil, and garnish with additional black pepper.