Bring broth and oil to a boil in a small saucepan. Add cornmeal, stirring constantly with a whisk until cornmeal begins to absorb liquid (about 2 minutes). Reduce heat to low; cook 25 minutes, stirring frequently. Remove from heat; stir in cheese.
Spoon cornmeal mixture into a 2-quart baking dish coated with cooking spray. Using a spatula coated with cooking spray, spread into an even layer. Cool to room temperature; cover and chill overnight.
Preheat oven to 400°.
Cut polenta into 20 pieces. Arrange in a single layer on a baking sheet coated with cooking spray. Bake at 400° 30 minutes, turning after 15 minutes. Cool to room temperature on a wire rack.