Step 1

Preheat oven to 425 degrees. Brush a shallow 2-quart baking dish with oil. Bring milk and 2 1/2 cups water to a simmer in a medium pot. Whisk in polenta; cook, whisking, 1 minute. Season with salt and pepper. Transfer to prepared dish, spreading in an even layer.

Step 2

Layer half of leek, eggplant, zucchini, and tomatoes over polenta. Drizzle with 3 tablespoons oil; season with salt and pepper. Scatter with half of cheese. Repeat layering with remaining ingredients, omitting cheese.

Step 3

Bake 30 minutes. Press vegetables down with a spatula; sprinkle with remaining cheese. Bake until vegetables are knife-tender and edges are caramelized, about 35 minutes more. (If cheese is darkening too quickly, tent with foil.) Let cool slightly before serving.