Add bread ingredients to bread machine pan in the order suggested by manufacturer. Select dough/manual cycle.
When cycle is complete, remove dough from machine to a lightly floured surface. If necessary, knead in enough flour to make dough easy to handle. Divide dough into 20 equal pieces. Form each piece into a smooth ball. Stir together the 1/3 cup sugar and cinnamon. Dip each ball into the 2 tablespoons melted butter; roll each ball in sugar mixture.
Arrange half of the coated balls in the bottom of a greased 6 1/2- to 8-cup ovenproof ring mold or fluted tube pan with nonremovable bottom. Make a second layer, positioning the balls for the second layer between the balls in the first layer.
Drizzle balls with any remaining melted butter and sprinkle with any remaining sugar mixture. Cover and let rise in a warm, draft-free place until almost doubled in size, 30 to 45 minutes.
Bake at 350°F for 20 to 25 minutes or until done. Cool 1 minute on a wire rack. Invert onto a serving plate; remove ring mold or pan. Serve warm.