Bring the chicken stock and 1 1/2 cups water to a boil in a pot. Reduce the heat to a simmer and gradually whisk in the cornmeal. Cook, stirring, until tender, 30 to 35 minutes (the polenta should still be thin enough to pour). Stir in the butter, parsley, nutmeg and salt and pepper to taste.
Butter a baking dish. Pour in one-quarter of the polenta and top with 1 kind of diced cheese of your choice. Add another quarter of the polenta followed by another diced cheese. Add another layer of polenta and the remaining diced cheese. Top with the remaining polenta and sprinkle with the Parmigiano-Reggiano. Garnish with the rosemary and tomatoes. (If you are not serving immediately, let the casserole cool, then cover and refrigerate. To reheat, bring to room temperature, then bake as directed. It may take an extra 10 to 15 minutes.)
Bake the casserole until golden, 20 to 30 minutes.
If you have any leftovers, fry the polenta and serve it the next morning with eggs.