Using a medium-sized saucepan, combine milk, salt, and nutmeg.
Place saucepan in medium-high heat and bring to a boil.
When you see that the milk is close to boiling (bubbles are forming on the side of the pan), slowly add the semolina flour while whisking.
Adjust heat to medium-low and continue whisking until the semolina starts pulling from the sides. It's easier to use a rubber spatula or wooden spoon instead of a whisk at this stage. This should take you about 10 minutes.
Take the saucepan out of the heat.
Using a small bowl, combine and mix the yolk, half of the melted butter, and half of the grated Parmigiano.
Add this yolk mixture into the semolina and mix thoroughly.
Line your small oven tray with plastic and spread the mixture evenly on it. Use an angled spatula to even out the top. It should be about 1 to 1.5 cm thick.
Place the tray in the refrigerator for about 60 to 90 minutes. Depending on how cold your refrigerator is, the mixture should already be quite solid by this time.