This tasty recipe for polenta gratin is courtesy of Tom Colicchio.
In a large skillet, heat vegetable oil over medium-high heat. Add onion, carrot, and celery; season with salt and pepper; cook, stirring occasionally, until vegetables begin to soften, about 5 minutes.
Add garlic and cook for 1 minute. Add mushrooms and thyme leaves; cook, stirring frequently, until mushrooms are almost tender, about 3 minutes. Add tomato and cook, about 2 minutes more.
Add stock to skillet, 2 tablespoons at a time, bringing liquid to a simmer before each addition. Simmer until thickened, about 30 minutes. Remove from heat and set mushroom bolognese aside to cool.
In a medium bowl, mix polenta with 2 tablespoons water to moisten. Bring 4 cups water to a boil in a medium saucepan over high heat. Add a pinch of salt to boiling water and slowly stir in polenta. Bring to a boil, stirring constantly, and immediately reduce to a simmer. Cook polenta, stirring occasionally, until no longer grainy, about 30 minutes. Remove from heat; stir in olive oil and season with salt.
Preheat oven to 350 degrees. Spoon half of the polenta into a medium baking dish and cover with reserved mushroom bolognese. Top with remaining polenta and sprinkle with Parmigiano Reggiano.
Transfer baking dish to oven and bake until top is golden, about 40 minutes. Serve immediately.