Step 1

Heat the oven to 375°F with racks in the upper- and lower-middle positions. In a Dutch oven, whisk together the polenta, 2 teaspoons salt and 6½ cups water. Bring to a gentle simmer over medium-high, whisking often. Transfer the pot, uncovered, to the lower oven rack and bake for 45 minutes. Meanwhile, coat an 8-inch square baking dish with 1 tablespoon of the butter. In a medium bowl, toss together both cheeses.

Step 2

Remove the pot from the oven. Increase the oven to 425°F. Whisk the remaining 2 tablespoons butter and ½ teaspoon pepper into the polenta. Use a wooden spoon to scrape along the bottom and into the corners of the pot.

Step 3

Transfer about 2 cups of the hot polenta to the prepared baking dish and spread in an even layer. Sprinkle evenly with one-third of the cheese mixture. Spread half of the remaining polenta over the cheese, then sprinkle with half of the remaining cheese mixture. Finally, spread the remaining polenta on top. Add the sour cream and spread in an even layer. Sprinkle evenly with the remaining cheese.

Step 4

Bake, uncovered, on the upper rack until the edges are bubbling and the surface is spottily browned, 20 to 25 minutes. Cool for 10 minutes before serving.