This is a recipe from a friend of mine, Ethan Stowell. He is the chef and owner of a bunch of Italian-focused restaurants in Seattle. One of his restaurants, Rione XIII, is focused solely on Roman cuisine. While many gnocchi are cooked in simmering water, gnocchi alla romana — Roman gnocchi—are made from cooking semolina in milk, similar to making polenta, and later baking the dumplings in an oven, preferably a wood-fired one. Modern, health-conscious Italians are backing off from finishing the semolina with butter, using olive oil instead. — Jenn Louis, author of Pasta By Hand: A Collection of Italy’s Regional Hand-Shaped Pasta.
In a 4-quart saucepan, bring the milk to a boil over medium-high heat. Turn the heat to low and add the semolina flour, pouring it in a steady stream and whisking constantly. Once the semolina has been whisked in and there are no lumps, switch to a wooden spoon and continue to stir for 2 minutes. Remove from the heat, stir in the egg yolks, one at a time, and then add half of the Parmigiano-Reggiano cheese. Season with salt and nutmeg.
Butter a baking sheet. Pour the semolina mixture onto the prepared baking sheet and smear to a thickness of about 1 inch. Let cool to room temperature, then cover with plastic wrap and refrigerate until cold and firm, preferably overnight.
Preheat the oven to 400 degrees F. Use 2 tablespoons of the butter to grease a 9-by-13-inch baking dish or 6 individual gratin dishes.
Using a 2-inch round pastry cutter, cut out circles of dough. Arrange the circles in the buttered baking dish or gratin dishes, overlapping them slightly, and sprinkle with the remaining 6 tablespoons butter and the remaining Parmigiano-Reggiano, evenly dividing the butter and cheese if using individual dishes. (Gnocchi alla romana can be refrigerated for up to 3 days, covered with plastic wrap, before topping with butter and cheese and baking.) Bake until the butter and cheese are melted and the tops of the gnocchi are a rich golden brown, 10 to 15 minutes. Serve right away.