Preheat the oven to 400°F. Cut the squash in half, remove seeds, and place face-down on a parchment-lined sheet. Drizzle garlic with olive oil, wrap in foil, and roast both for 30 minutes until soft.
Scoop roasted squash and garlic into a blender with vegetable stock. Blend until smooth to form a creamy, sweet base. Set aside for the next step.
In a large pot, heat olive oil and sauté half of the brussel sprouts until slightly charred. Remove, then sauté onions with rosemary and thyme until softened and fragrant.
Add white wine if using and cook off alcohol. Stir in Calabrian chili paste, the blended squash broth, butter beans, and seasonings. Simmer to combine flavors and slightly thicken the broth.
Return sautéed brussel sprouts to the pot, taste, and adjust salt and pepper. Drizzle red wine vinegar for brightness, then serve warm, garnished with fresh herbs or a crusty slice of bread.