Step 1

Bring milk and 3 cups stock to a boil in a large saucepan. Whisk in polenta. Reduce heat to low and cook, whisking occasionally, until polenta is tender, 15 to 20 minutes. Whisk in cheese and butter until melted. Season with salt and pepper.

Step 2

Meanwhile, heat oil in large skillet over medium-high heat. Add mushrooms and shallot and cook, stirring occasionally, until mushrooms are golden brown, 10 to 12 minutes. Stir in tomatoes, collards, garlic, and remaining 1/4 cup stock. Cook, stirring occasionally, until greens are wilted, 4 to 6 minutes. Stir in vinegar. Season with salt and pepper.

Step 3

Serve mushroom mixture over polenta topped with additional cheese.