Heat the oil in a large skillet over medium heat. Add the garlic and cook 30 seconds, then stir in the Swiss chard stems. Pour in a few tablespoons of water and cover the pan. Cook the stems 2 minutes. Remove the cover, the mix in the Swiss chard leaves. Cover the pan again and cook until the leaves wilt, about 3 minutes. Toss occasionally. Remove the pan from the heat and let cool, uncovered.
To make the polenta preheat the oven to 400 degrees. Butter a 2 1/2quart shallow baking dish and set it nearby. Combine the milk, water, and salt in a mediumsize saucepan and bring to a boil. Reduce the heat to mediumlow and slowly drizzle in the cornmeal, whisking all the while with a wire whisk. Continue to cook and whisk the polenta until it is the consistency of mashed potatoes and tears away from the sides of the pan, about 5 minutes. Whisk in 2 tablespoons of the Parmesan cheese, the 1 tablespoon of butter, and the mozzarella cheese.
Spread half the polenta in the baking dish. Spoon on the Swiss chard and distribute it evenly. Drop on small spoonfuls of the sour cream and spread it with the back of a spoon. Spoon on the remaining polenta and spread it out. Sprinkle on the remaining tablespoon of Parmesan cheese. (The casserole may be prepared to this point and refrigerated up to 24 hours in advance. Bring to room temperature before baking.)
Bake the polenta for 20 to 25 minutes, or until golden on top and sizzling. Do not overcook it because you want to retain its creamy interior.