Preheat the oven to 400F. Grease an ovenproof dish with butter.
Pour the milk into a pan, add the salt, and bring to a boil. As soon as the milk simmer, add the semolina flour while whisking constantly with a long wooden spoon to prevent lumps from forming.
When all the flour has been incorporated, keep cooking and stirring with the wooden spoon reaching to the bottom of the pan. About 10 minutes. The semolina is cooked when it sticks heavily to the spoon and comes away clean from the sides of the pan.
Let cool slightly, then stir in half of the butter, half of the Parmigiano, and both eggs. Mix until all is well incorporated.
Pour the semolina over parchment paper and spread the mixture out to ½ inch thick with a damp knife or wet spatula.
Stamp out the 2-inch round with a cookie cutter and place a layer of those rounds in the prepared ovenproof dish, slightly overlapping one another.
Brush the rounds with the remaining butter and sprinkle with the remaining ½ cup Parmigiano.(This dish can be prepared up to this point a few days ahead, covered, and refrigerated)
Bake in the middle rack of the oven until the gnocchi has a golden color. 10-15 minutes. Let stand 5 minutes before serving.