How to Make It
Cook polenta according to package directions. Remove from heat. Stir in 1 cup cheese and ½ teaspoon salt, stirring until cheese is melted and polenta is smooth; cover and set aside.
Melt 2 tablespoons butter in a large nonstick skillet over medium-high. Add mushrooms and thyme and cook, stirring occasionally, until golden, 6 to 8 minutes. Add tomatoes, pepper, and remaining 1 teaspoon salt. Cook until tomatoes burst, about 5 minutes. Add wine and bring to a simmer. Cook until mostly reduced, 5 to 6 minutes. Stir in remaining 2 tablespoons butter to melt.
Spoon mushroom mixture over polenta and top with remaining ½ cup cheese.