Lightly coat a large rimmed baking sheet with 1 tbsp oil. In a large pot, bring milk, 3 cups water and salt to boil over high heat. Whisk in cornmeal in a gentle stream and reduce heat to medium-low. Simmer, stirring often, until polenta is thick and no longer gritty, about 20 minutes. Working quickly, pour polenta into prepared pan, spreading evenly to the edges. Let stand 10 minutes; cover with plastic wrap and press polenta along sides of pan to form edges of crust. Refrigerate at least 2 hours or overnight.
Heat oven to 450°. Bake chilled crust until it begins to brown at edges, 45 minutes to an hour. Heat remaining 1 tbsp oil in a large saucepan. Sauté shallots and garlic over medium-high heat until soft, 3 minutes. Add tomatoes and cook, stirring occasionally, until they begin to soften, 5 minutes. Mash with the back of a spoon and cook until thickened, 3 minutes more. Season with salt and pepper. Spoon sauce onto the crust, top with cheese and bake until cheese is bubbling, 10 to 15 minutes. Top with basil and cut into squares.