Melt 1/4 cup butter in a Dutch oven over medium heat; add onion, celery, and garlic, and sauté 3 to 5 minutes or until tender. Add broth, and bring to a boil; gradually stir in cornmeal and next 3 ingredients. Reduce heat to low, and cook, stirring often, 10 minutes. Remove from heat, and stir in cheese.
Pour mixture into a lightly greased 13- x 9-inch baking dish; cover and chill 3 to 12 hours or until firm. Cut polenta into 12 triangles.
Melt 1 Tbsp. butter in a large nonstick skillet over medium-high heat. Add 3 polenta triangles, and cook 2 to 3 minutes on each side or until golden brown. Transfer to a serving dish, and keep warm. Repeat procedure with remaining polenta and 3 Tbsp. butter.