Preheat oven to 350 degrees. Heat 1 tablespoon of olive oil in a large skillet. Add the mushrooms and cook for about 5 minutes. Add the shallot and cook another 3 minutes. Add the spinach and thyme and saute until wilted. Season with salt and pepper.
In a small saucepan, melt the butter. Stir in flour. Add the broth and cream. Season with salt and pepper.
Place spinach in the bottom of a buttered casserole dish. Pour sauce over the top. Place circles of polenta on top of spinach, pressing down. Top with cheese, cover and bake for 40 minutes. Remove cover and broil until top is brown, abiout 2 minutes. Let rest for a few minutes before serving.