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Step 1
Heat the milk in a large saucepan over medium-high heat until tiny bubbles start to form around the edges of the pan and the liquid is just short of boiling.
Step 2
Reduce the heat to low and slowly add the semolina flour in a thin steady stream with one hand as you stir the mixture steadily with a large stiff whisk. Cook the mixture for roughly 15 to 20 minutes total, or until it becomes very thick and begins to pull away from the sides of the pan. It will be very loose for the first few minutes and will thicken to the consistency of a loose pudding within about 5 minutes. Once the mixture is thick enough that it becomes difficult to continue whisking, switch to a wooden spoon. Continue stirring with a wooden spoon, scraping the sides of the pan as well, until the mixture begins to form a loose-ish mass and begins to pull away from the sides (approximately 15 to 20 minutes of total cook time ). Remove from the heat. Allow the mixture to cool for a minute or two.
Step 3
Stir in ⅔ of the grated parmesan cheeses, 2 tablespoons (30 g) unsalted butter, freshly grated nutmeg, and kosher salt. Season to taste, adding more salt and freshly ground black pepper as needed. Once the mixture has cooled just slightly, add the egg yolks and mix rapidly with a wooden spoon until fully incorporated.
Step 4
Moisten a half sheet pan with cold water over a sink and allow the excess water to drip off the pan. Spoon the hot semolina mixture onto the moistened sheet pan, spreading it with an offset spatula into an even layer until it is just under ½-inch thick. Let cool for 30 to 40 minutes.
Step 5
Preheat the oven to 425°F (220°C) with a rack in the center position. Grease the bottom and sides of an oven-safe baking dish (roughly 2 quarts in capacity) with unsalted butter. Using a small biscuit cutter (roughly 2½-inch in diameter), cut the semolina into disks, dipping the biscuit cutter into water between each cut to prevent sticking. Transfer and layer the semolina rounds into the greased baking dish, overlapping the slices slightly, so that each row resembles roof shingles. Top with the polenta with the remaining 2 tablespoons (30 g) butter, cut into small cubes. Sprinkle the dish with the remaining grated cheese. Make Ahead Tip: Gnocchi alla romana can be prepped ahead to this stage and stored, covered with plastic wrap, in the refrigerator for up to 2 days.
Step 6
Bake uncovered for 15 to 20 minutes or until a light golden crust is formed. Allow to cool for a few minutes before serving.