Prep Time: 35 minutes
Preheat the oven to 400 degrees. In a large mixing bowl, combine the carrots with 1 Tbsp. oil and season with a pinch of salt and pepper. Place in the oven on a baking sheet until the carrots are slightly browned and cooked through, turning once, about 30 minutes.
While the carrots are cooking, prepare the polenta and leeks. For the polenta, over a high flame boil the water in a large pot with a lid. Season with a pinch of salt and whisk in the polenta, making sure to break up any clumps that form. Reduce the heat to low and continue cooking while stirring, until slightly thickened, about 5 minutes. Cover and continue to cook until the polenta is creamy and thick, stirring occasionally, about 20 minutes. When finished, stir in the butter, until melted, and season with a pinch of salt and pepper, to taste.
For the leeks, heat 1 1/2 Tbsp. oil in a large sauté pan. Add the leeks and season with a pinch of salt. Reduce the heat to medium and continue to cook while stirring occasionally until the leeks are completely soft and "melted," about 20 minutes.Divide the polenta among 4 plates. Top evenly with the roasted carrots and leeks. Garnish each plate with Gruyère.