While the mushrooms are roasting, make the polenta. In a medium saucepan, combine milk, water, and salt over medium-high heat and bring to a simmer. When it simmers, slowly pour in the polenta and whisk to combine. Reduce heat to low and partially cover the pan with a lid and cook, whisking vigorously every 5 minutes. Make sure you scrape the sides of the pan. Cook until liquid is absorbed and polenta is creamy, about 30 minutes total. Remove from heat and stir in the butter and Parmesan cheese.