Preheat oven to 425°F.
Heat olive oil in a large, 12- to 14-inch skillet. Add mushrooms and brown; add beef and sausage, and brown and crumble. Add onions, garlic and sage to meat and mushrooms, and stir 2-3 minutes. Stir in tomato paste, cook 1 minute more; add wine to deglaze the pan. Add 1 cup stock, reduce heat to a low simmer and cook a few minutes to thicken and combine flavors. Transfer sauce to a bowl.
Rinse skillet and return it to heat. Add remaining 3 cups stock and 1 cup milk, and bring to a simmer. Lower heat to medium-low and whisk in polenta. Stir 15-18 minutes to thicken then season with salt, pepper and nutmeg. Turn off heat and add in butter, honey and half the grated cheeses. Smooth polenta and make a well in the center, about an inch from the edge of pan. Fill trough with meat sauce and top with dollops of ricotta. Sprinkle remaining grated cheeses over the top, bake a few minutes to brown then serve from skillet at the table.
This skillet supper is a weeknight alternative to lasagna.