Heat a large skillet over high heat and add the sausage, breaking it down with a wooden spoon. Cook for about 5 to 7 minutes, until the sausage has browned and crisped. Add in the onions and mushrooms and cook until softened. Season with 1 teaspoon salt and 1 teaspoon black pepper. Reduce heat to low.

To make the polenta, bring the water, milk, and 1 teaspoon salt to a simmer in a medium pot. Slowly stream in the cornmeal while whisking. Reduce the heat to low and continue to cook (stirring often) until mixture is thick and creamy, about 20 minutes. Remove from heat and stir in the butter, cheese and 1/2 teaspoon black pepper. Stir until melted.

Serve with sausage and mushrooms spooned on top. Garnish with scallions.