Whisk the stock, semolina flour, and salt in a heavy medium saucepan over medium-high heat until the mixture bubbles and is very thick, about 10 minutes. Beat the egg in a large bowl. Gradually beat the semolina mixture into the egg.
Transfer the gnocchi mixture to the prepared baking sheet, spreading it to form a 1/2-inch-thick layer. Cover and refrigerate until the gnocchi mixture is cold and firm, at least 1 hour.
Preheat the broiler. Generously butter a 10-inch-diameter gratin dish. Using a 2-inch-diameter cookie cutter, cut out rounds from the gnocchi mixture. Arrange the gnocchi in the prepared baking/gratin dish, overlapping slightly.
Brush the remaining butter over the gnocchi.
Sprinkle with the cheese, and pepper, if desired. Broil until the gnocchi are heated through and beginning to brown, about 6 minutes.
