Rainy showers bring wild mushrooms, which sauté quickly into a silky sauce. Spoon them into warm bowls with creamy polenta and a dusting of cheese.
Allergen Note: Contains milk, eggs.
In a small pot, bring 3 cups water and a pinch of salt to a simmer. In a bowl, whisk together 1 cup polenta, 1 cup milk, and a pinch of salt and let soak. When the water is simmering, whisk in the polenta, along with the soaking liquid. Turn down the heat to low, cover, and simmer until tender, stirring occasionally, about 10 minutes. Remove from the heat and whisk in 1 tablespoon butter and ½ teaspoon salt.
Meanwhile, to clean the mushrooms, depending on the variety, either brush away any pine needles or grit, or if they have hollow centers, split them in half and quickly rinse to remove any grit inside. Tear or slice the mushrooms into bite-size pieces. Slice the shallot. Chop 2 or 3 cloves of garlic.
In a large sauté pan over medium heat, warm 2 tablespoons olive oil. Add the mushrooms and sauté until they release their moisture and start to brown, about 8 minutes. Add the shallot and garlic and stir until fragrant, 1 minute. Add ¾ cup broth, wine, or water and a few sprigs of thyme and simmer until the liquid has reduced by about half, 3 to 5 minutes. Add 2 tablespoons butter and stir until melted and glossy. Remove and discard the thyme sprigs. Season to taste with salt.
Just before serving, in a nonstick frying pan over medium-high heat, warm 1 teaspoon olive oil. Add 3 eggs and fry until done to your liking, 3 minutes for sunny-side up.
Spoon the polenta and creamy wild mushrooms into bowls and slide the eggs on top. Sprinkle with Parmesan, if you have some on hand, grind with pepper, and serve warm.