In a heavy-bottomed pot, on medium-high heat, bring the milk to a boil and season with salt.
Turn the heat down to medium-low. Pour the semolina into the milk in a steady stream, whisking constantly until it has all been added. Simmer, whisking often, until the semolina starts to get thick and almost cooks. Switch to a wooden spoon and keep stirring until the semolina is cooked, approximately 20 minutes.
Remove the pot from the heat and blend in 3 oz. of the butter, the egg yolks, and 3 oz of grated parmesan.
Shape the gnocchi mixture into quenelles or roll into index finger thick tubes and cut into 3/4 inch “logs”. After repeating this with all of the batter, roll the end of the log with the tines of a fork, using your thumb.
To serve the gnocchi, transfer them to a liberally buttered baking dish. Brush or drizzle with the remaining butter and the sausage with the cheese. Bake in a 400ºF oven or brown under a broiler for 5 to 6 minutes. Serve immediately.