Melt 1/4 cup butter in a large saucepan over medium-high heat; add garlic, and sauté until tender. Stir in broth; bring to a boil. Whisk in cornmeal until smooth. Reduce heat; simmer, uncovered, 10 minutes, stirring often. Stir in cheese and next 3 ingredients. Pour mixture into a lightly greased 13- x 9-inch pan; cover and chill at least 8 hours.
Cut polenta into 6 squares; cut each square into 2 triangles. Melt 2 tablespoons butter in a large skillet over medium-high heat. Cook half of triangles 4 minutes on each side or until lightly browned. Repeat procedure with remaining 2 tablespoons butter and polenta. Serve immediately.