Spread mixture evenly over bottom of a 2-quart casserole.
Melt butter in a small saucepan. Whisk in flour, and cook over medium-high heat. Add broth and cream and whisk until thickened, about 5 minutes. Season lightly with salt and pepper and pour over spinach.
Arrange polenta slices on top of spinach and sauce in overlapping concentric circles, pressing to submerge polenta slightly. Sprinkle shredded cheeses over polenta. Cover with foil and bake 30 minutes. Remove from oven and preheat broiler.
Uncover polenta and broil 6 inches from heat about 2 minutes or until browned and bubbly. Let stand 10 minutes before serving.