Preheat the oven 350°F and set a rack in the middle position of the oven.
Use a 9x13-inch casserole dish that has a lid. Add the cornmeal to the dish and add the chicken broth and water, stir to combine. Add the butter. Cover and place in the oven to cook for 45 minutes.
Remove the polenta from the oven and stir to mix in any butter that is still floating on the top. The polenta should be soft like the texture of thick yogurt.
Smooth the top of the polenta out. Pour the heavy cream over the top of the polenta in one even layer. Scatter the parmesan cheese over the cream, in one even layer.
Set the broiler to low. Place the polenta under the broil and cook for 4-6 minutes until the top is starting to turn golden brown. Remove from the oven and cool for a few minutes before serving.
