Preheat the oven to 400F.
Place the halved acorn squash or pumpkin on a sheet pan or roasting rack. Spread one tbsp of butter on each half and sprinkle evenly with brown sugar. Season with salt and pepper. Roast for 45-50 minutes until very tender. Let cool and scoop out the flesh with a spoon.
Meanwhile, heat a saucepan over medium heat. Add one tbsp butter and the oil. Once hot, add the minced garlic and sliced leeks. Cook for 3-5 minutes until soft.
Add the diced carrots, apples, cooked squash or pumpkin, and sage. Add the stock and bring the soup to a boil. Turn it back down to a simmer and cook until the carrots and apples are tender.
Once tender, puree the mixture until smooth in a blender. Season for salt and pepper. Garnish with croutons and chopped crisp sage.