Cheesy Baked Polenta

I have been planning for some time to make an attempt at polenta and this is what I came up with.  I cooked it half on the stove top and half in the oven.

1 tablespoon olive oil
1/2 cup finely diced onions
1 teaspoon dried thyme
1 teaspoon sea salt
1/4 teaspoon ground black pepper
5 cups water, divided
1 1/2 cup yellow cornmeal
4 ounces asagio cheese, very thinly sliced and divided
4 ounces mozzarella cheese, very thinly sliced and divided
1/2 cup grated Parmesan cheese
1/2 cup milk

1. Preheat the oven to 350 degrees and grease a 2 quart baking dish.
2. Warm the oil in a medium sized saucepan over medium heat. Add the onion and cook until translucent, about 5 minutes.  Add the thyme, salt, pepper and 3 cups of water and bring to a boil.  
3. In a separate boil stir together the remaining 2 cups of water with the 1 1/2 cups cornmeal.  Gradually add this to the boiling water.  Stirring constantly cook until the cornmeal mixture is very thick.  
4. Pour half the polenta into the prepared baking dish, and smooth with an off set spatula.  Top the layer of polenta with half of the asagio and mozzarella cheeses.  Top with the remaining polenta, and smooth with off set spatula.  Top with remaining cheeses.  Pour the milk over the layer of cheese, carefully place in the oven and bake for 35-45 minutes.  Let stand for 10 minutes before serving.