Preheat oven to 375°F Arrange squash, cut side up, in large roasting pan. Place garlic cloves in squash cavities. Drizzle oil over. Sprinkle with dried sage, salt and pepper. Bake until squash is tender, about 1 hour 30 minutes. Cool slightly. Peel squash and garlic. Transfer to processor and puree.
Combine broth, 1 3/4 cups water and 1 1/2 teaspoons salt in heavy large saucepan. Bring to boil. Gradually whisk in polenta. Reduce heat to medium-low and cook until mixture is very thick and creamy, stirring often, about 20 minutes.
Stir in fresh sage and 3 cups squash puree (reserve any remaining puree for another use). Cook until heated through, about 2 minutes. Stir in cheese. Season with salt and pepper.