How to Make It
Bring the milk, 2 cups water, ½ teaspoon salt, and ¼ teaspoon pepper to a boil in a medium pot. Slowly whisk in the polenta. Cook, whisking constantly, until the polenta thickens, 3 to 4 minutes. Remove from heat and stir in the Parmesan.
Melt the butter in a large skillet over medium-high heat. Add the mushrooms and cook, stirring occasionally, until browned, 4 to 6 minutes. Add the shallot and thyme. Cook, stirring, until the shallot is softened, 1 to 2 minutes. Add the marinara and simmer, about 1 minute.
Spoon the mushrooms and sauce over the polenta and serve topped with additional Parmesan.