Preheat the oven to 400F. Place tomatoes in a roasting pan, baking dish or baking sheet cut-side up. Drizzle with oil then add garlic. Sprinkle with salt and pepper and top with fresh oregano leaves. Roast in the oven until the tomatoes are very tender, about 30 minutes. When tomatoes are very tender, remove from oven and cool at room temperature for 5 minutes. Peel off and discard the stems then mash the tomatoes and garlic to desired consistency.
Meanwhile, bring water to a boil in a medium saucepan over medium-high heat. Slowly whisk in cornmeal then reduce heat to maintain a low simmer. Cook, stirring occasionally, until the polenta is very tender, about 30 minutes. Be sure the mixture is barely simmering and you stir occasionally to prevent scorching.
Stir in the cream or milk, butter and cheese along with half of the roasted smashed tomatoes. Adjust seasoning with more salt and pepper, if desired. Serve the cheesy polenta topped with more of the tomato sauce, more cheese and oregano, if desired.
