1. Heat oven to 350 degree F. Grease a 3-quart rectangular baking dish and set aside. In a medium saucepan over medium heat, melt the butter. Add shallots and cook until translucent, 5 minutes. Stir in 1-1/2 cups chicken broth, 1-1/2 cups water, and salt, and bring to a boil.
2. Meanwhile, in a large saucepan on low heat, slowly add the cornmeal, remaining chicken broth and 1 cup water, stirring until well combined. Gradually stir in the boiling butter-shallot-broth mixture and cook, stirring constantly until the cornmeal is thickened, 15 minutes. Pour half of this polenta mixture into prepared baking dish, smoothing evenly with a spatula. Sprinkle 1/2 cup Parmesan cheese and sage evenly over top. Add remaining polenta, spreading evenly, and sprinkle with remaining Parmesan cheese. Drizzle with cream and bake until the top is flecked with brown, 35 to 45 minutes. Cool completely in the pan, then refrigerate until cool, about 1 hour.
3. Prepare a covered grill for direct grilling. When the polenta is firm, cut into 2 inch squares and grill over a low flame until grill marks appear, about 2 minutes, then turn and grill until marked on the other side, 2 minutes more. Makes 6 to 8 servings.