In large bowl, mix 1 cup of the flour, 1 cup cornmeal, the sugar, salt and yeast. In 1-quart saucepan, heat water and 1/4 cup butter until hot (120°F to 130°F). Add hot liquid to flour mixture; beat with electric mixer on low speed until moistened, scraping bowl frequently. Beat on medium speed 2 minutes, scraping bowl frequently. With spoon, stir in 1/2 to 1 cup of the flour until dough pulls away from side of bowl.
On floured work surface, knead in remaining 1/4 cup flour until dough is smooth and elastic, about 2 minutes. Grease large bowl with shortening or cooking spray. Place dough in bowl; cover loosely with plastic wrap and cloth towel. Let rise in warm place (80°F to 85°F) about 10 minutes or until light and doubled in size.
Grease 2 large cookie sheets with shortening or cooking spray; sprinkle with cornmeal. Gently push fist into dough to deflate; divide dough into 24 pieces. Roll each piece into 10-inch rope; place on cookie sheets. Cover; let rise in warm place about 10 minutes or until light and doubled in size.
Heat oven to 375°F. Uncover dough. Carefully brush sticks with 2 tablespoons melted butter; sprinkle with 2 tablespoons cornmeal. Bake 12 to 16 minutes or until bottoms are golden brown. Immediately remove from cookie sheets. Serve warm or cool.