Preheat oven to 425°F.
Butter a nonstick, regular-size muffin tin.
Bring the milk and stock to a bubble in a medium-sized stockpot over medium heat. Slowly whisk in the polenta and continue whisking until it begins to thicken and resemble hot oatmeal, about 3-4 minutes. Turn off the heat, add in the cheese and season with salt and pepper.
While the milk and stock are coming up to a bubble, place the sausages and grapes on a baking sheet. Drizzle them with EVOO and season with pepper. Pour the balsamic over everything and pop the baking sheet into the oven for 20-25 minutes.