Souffléed Gnocchi

Bring milk with salt to a simmer in a 2- to 3-quart heavy saucepan over moderately low heat. Add semolina in a slow stream, whisking, then simmer, stirring constantly with a wooden spoon, 12 minutes (mixture will be very stiff). Remove from heat and stir in eggs 1 at a time, then stir in 6 tablespoons cheese and 3 tablespoons butter. Spread gnocchi mixture into a 1/2-inch-thick slab on an oiled baking sheet using a lightly oiled rubber spatula, then chill, uncovered, until cool to the touch, about 10 minutes.
Cut out rounds from gnocchi mixture with cookie cutter dipped in cool water (incorporating scraps as you work) and gently transfer rounds (they will be very soft), slightly overlapping, to buttered baking dish. Chill gnocchi, uncovered, 1 hour.
Put oven racks in upper and lower thirds of oven and preheat oven to 450°F.
Melt remaining 1 1/2 tablespoons butter and brush over gnocchi, then sprinkle with remaining tablespoon cheese.
Bake in upper third of oven 10 minutes, then switch dish to lower third of oven and continue to bake until gnocchi are slightly puffed and lightly browned, about 10 minutes more. Let stand 5 minutes before serving.
Unbaked gnocchi can be chilled up to 1 day, covered after 1 hour.