1. Add the olive oil to a sauté pan and heat. Add the shallot and a pinch of salt and sweat until it is translucent. Add the garlic and cook until you can just smell it.
2. Increase the heat and add the chopped mushrooms, thyme, salt and pepper and sauté until the mushroom liquid evaporates and the mushrooms are nicely brown and tender.
3. Add some of the stock to deglaze the pan and keep the mushrooms from drying out.
4. If desired, finish the dish with a little cream, heat through and reduce slightly and serve.
5. Heat 2 cups of the half and half in a large saucepan. Add a pinch of salt and a few grinds of pepper.
6. When the half and half comes to a boil, reduce the heat and very gradually add the cornmeal, whisking constantly.
7. Continue to whisk until all of the cornmeal is incorporated. Once the meal has been added, switch to a wooden spoon and continue to cook, stirring, over low heat for 10 minutes or so.
4. Stir in the Parmesan and season the polenta well with salt and pepper. Add the reserved ¼ cup of half and half as necessary. The polenta should be creamy, not stiff. Serve hot and top with the mushroom ragout.