Clean the mushrooms, trim the stems, and cut them into 1/4-inch slices. Set aside.
Soak the dried mushrooms in the warm water until softened and rehydrated, 20 to 25 minutes. Strain the soaking liquid, reserving 1/2 cup and blot the mushrooms dry. Chop roughly and set aside.
Tip: When you're using the soaking liquid from dried mushrooms in your recipe, it's best to use a shallow bowl for soaking. This allows you to use less water, resulting in more flavorful liquid.
Make the polenta:
While the mushrooms soak, prepare the polenta. Melt the butter in a saucepan over medium-high heat. Add the garlic, sauté 1 minute, then add the milk, chicken broth and salt and pepper and bring to a boil. Add the cornmeal, whisking constantly until well blended.
Reduce the heat to low and cook 8 to 10 minutes, continuing to whisk frequently until thickened. Add the sage and goat cheese and stir until smooth. Remove from the heat and cover to keep warm.
Cook the mushrooms:
In a large skillet, heat the butter and olive oil over medium heat. Add the onion and sauté until softened, 2 to 3 minutes. Add the garlic and continue cooking for 1 minute longer.
Begin adding the mushrooms, a couple of handfuls at a time, and sauté each batch until slightly softened before adding more. Once all the mushrooms are in the skillet, season to taste with salt and pepper. Continue cooking, stirring frequently, for 5 to 6 minutes.
Stir in the reserved mushroom liquid and sherry, increase the heat to medium-high and simmer the mixture, stirring often, until the liquid has reduced by 1/2, 3 to 4 minutes. Adjust the seasoning if necessary, then add the thyme, sage and cream. Cook for 1 minute longer.
To serve, plate a serving of polenta, top with mushrooms and spoon a little of the sauce over all.
Tips for Making This Recipe
About the mushrooms:
Your choice of mushrooms for this dish is flexible. You can combine several varieties of fresh mushrooms (we used white button, cremini and shiitake), or stick with just one. The dried mushrooms add depth of flavor to the dish and you can choose whatever variety you like best. We went with chantarelles because we love their unique shape and texture, but any variety will provide that earthy boost of flavor.