Cut the butternut squash in half lengthwise to remove the seeds and strings. Peel the skin using a paring knife and cut the squash into small cubes.
Place the olive oil and shallots in a deep skillet over medium heat. When the shallots begin to color, add the squash and season with salt and pepper. Saute a few minutes to lightly caramelize the surface of the cubes. Add the bay leaf, nutmeg, sage, and chicken broth. Cover the pan and cook until the squash is tender but still holding its shape, about 8 minutes.
Puree the sauce with a standard or immersion blender and serve with potato gnocchi. Top with grated cheese and chopped chestnuts before serving. If desired, fry some sage and shallots in olive oil to garnish.