Preheat oven to 325°F Cut each squash in half and remove seeds. Cut off rind with a small sharp knife. Cut squash into 1-inch cubes.
Peel carrots and cut into 1-inch pieces. Mix squash and carrots with 5 tablespoons apple butter, 1/2 teaspoons salt, and freshly ground black pepper. Place mixture on baking sheet big enough to accommodate vegetables in one layer. Add 3 tablesooons water and cover with foil.
Bake for 1 hour. Remove foil. Add 1/2 cup water and bake for 20 minutes more.
Transfer vegetables to food processor and process until very smooth. This must be done in several batches.
Transfer to medium pot. Add remaining 3 tablespoons apple butter and salt and pepper to taste. Reheat gently before serving. (This dish can also be made early in the day and reheated).