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.