Heat 1 cup water and 1/4 cup butter in a small saucepan until butter melts. Cool to 120° to 130°.
Combine 2 cups flour and next 6 ingredients in a large mixing bowl. Gradually add liquid mixture to flour mixture, beating at high speed with an electric mixer 1 minute. Add egg, and beat at medium speed 2 minutes. Gradually stir in 1/3 cup cheese and remaining 1 cup flour.
Cover and let rest 10 minutes. Place dough in a greased 2-quart round baking dish. Brush with melted butter, and sprinkle with remaining 1/3 cup cheese. Cover and let rise in a warm place (85°), free from drafts, 45 minutes (bread will not double in bulk).
Bake at 350° for 30 minutes or until golden. Cool in dish 10 minutes. Remove to a wire rack. Serve warm or at room temperature.
Note: Parmesan Bread may be frozen up to 1 month. Thaw, wrapped in aluminum foil, at room temperature; bake at 350º for 25 minutes just before serving.
Excellent bread with Southern Living's Lasagna Soup! Easy yeast bread since there really isn't any shaping to do! Will definitely make this one again!