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Lightly grease a 10" x 15" rimmed baking sheet. (If you only have a larger baking sheet, that’ll work, too; simply trace a 10" x15" rectangle on a sheet of parchment.)
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In a large saucepan over medium-high heat, bring the milk and water to a rolling simmer (just shy of a full boil), stirring occasionally. Reduce the heat to medium-low then gradually and steadily pour in the semolina while constantly stirring with a flexible spatula or whisk. Cook, still stirring constantly, until the semolina plumps and becomes very thick, with slow bubbles coming to the surface in the center of the pot, 2 to 4 minutes.
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Remove the pan from the heat and immediately stir in 2 tablespoons (28g) of the butter, 1 cup (100g) of the Parmesan, the salt, and nutmeg until well combined. Add the egg yolks and beat vigorously to fully incorporate.
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Working quickly, use a lightly moistened spatula to spread the warm semolina mixture onto the prepared 10" x 15" baking sheet in an even 1/2"-thick slab. (If working on a larger baking sheet, spread the mixture to fit the traced rectangle.) Cover loosely and let cool at room temperature until firm enough to cut, 25 to 30 minutes.
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Meanwhile, preheat the oven to 425°F and grease a 9" x 13" pan.
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Use a 2 1/2" round cutter to stamp out as many circles from the semolina as possible. Use a thin metal spatula or small offset spatula to carefully transfer the circles to the prepared pan, arranging the slices so they overlap like shingles. Press any scraps together to stamp out more circles. (Thirty circles will make a neat 5 x 6 arrangement.)
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Cube the remaining 2 tablespoons (28g) butter and scatter it over the top of the gnocchi, then sprinkle the remaining 1/2 cup (50g) Parmesan over the top.
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Bake the gnocchi alla romana for 22 to 28 minutes, until golden brown. Remove from the oven and let it cool slightly before serving.
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Store leftover gnocchi alla romana in an airtight container in the refrigerator for up to 4 days. Reheat in the oven, covered, before serving.
