Butter 9x13 inch baking dish. Combine 2 1/4 cups water, broth, shallots and marjoram in heavy large Dutch oven; bring to boil. Mix 2 1/2 cups cold water and cornmeal in bowl. Gradually mix cornmeal mixture into broth mixture. Return to boil, stirring constantly. Reduce heat to medium and boil gently until polenta is very thick, stirring often, about 10 minutes. Season with salt and pepper. .
Immediately spread 2 cups polenta in prepared dish. Top with 1 3/4 cups cheese. Drizzle with 1/4 cup cream. Repeat layering, using 2 cups polenta, 1 3/4 cups cheese, and 1/4 cup cream. Top with remaining polenta. Spread remaining cheese over. Cover with foil. (Can be made 1 day ahead. Cover and chill. Bring to room temperature before continuing.) .
Preheat oven to 350°F Bake covered polenta until hot in center, about 1 hour 15 minutes. Uncover; continue baking until polenta bubbles at edges and top begins to brown, about 10 minutes.