Grease a baking sheet and set aside.
Rinse the quinoa with cold water.
Place the quinoa in a small pot filled with 2/3 cup of water and bring to a boil.
Reduce the heat and let simmer uncovered until all the water is absorbed and set aside til ready to use.
Whisk together the milk, semolina flour and the salt in a sauce pan over medium-high heat until the mixture thickens and bubbles over for about 6 to 8 minutes while stirring constantly.
Remove the mixture from the heat and stir in the cooked quinoa, 2 tablespoons of butter, 1/2 cup grated Parmesan cheese and the beaten egg yolk.
Transfer the gnocchi mixture to your prepared baking sheet, spreading it out to about a 1/2 inch thick layer.
Chill uncovered for 1 hour or until very firm.
Butter a 10 inch round or oval shaped baking dish.
Using a 2 inch round cookie cutter or the top of a drinking glass, cut out round shaped circles from the firm gnocchi mixture.
Arrange the slices in the baking dish while slightly overlapping them.
Brush the 2 tablespoons of melted butter over the gnocchi and sprinkle with a 1/4 cup of grated Parmesan cheese.
Place the prepared gnocchi dish in the oven, on the middle rack and broil for about 8 minutes just until they have heated through and have a golden brown crust.