Remove the shells from chestnuts and blanch. Cut in halves, add 2 tablespoon butter and the sugar. Cover with boiling water and let cook gently until water has evaporated and the chestnuts are tender, but not soft.
Pick the wilted leaves from the sprouts, cut the stock close to the head and soak in cold salted water 1 hour or more. Drain well and cook rapidly in an uncovered kettle, in boiling salted water, 1 teaspoon to 2 quarts water until tender. Heat 2 tablespoons butter, add the flour, let brown slightly, add 1 cup of the sprout liquid and let cook until smooth. Add the chestnuts and sprouts, let heat through and serve.