Preheat oven to 375ºF.
Clean the mushrooms, remove the stems, and place them on a sheet pan underside up.
Sprinkle with olive oil and balsamic vinegar, sprinkle with salt and pepper. Bake for 20 minutes.
While mushrooms are cooking, make polenta. Bring chicken stock and milk to boil in a saucepan, lower the heat, and slowly sprinkle the cornmeal whisking constantly. Simmer for 6-7 minutes, whisking non-stop, until polenta is thick and smooth.
Remove from heat, stir in mascarpone, 1/2 teaspoon salt and pepper to taste.
Pour into 8 x 11 inch baking dish.
Arrange the mushrooms, underside up, in one layer over the polenta. Sprinkle on the gorgonzola, and bake for 25-30 minutes, or until the cheese is melted and browned.
Serve with fresh chives.