Melt the butter in a cooking pot over low heat, add flour, and continue stirring until you have a homogeneous mixture.
Cook for 2-3 minutes while stirring vigorously, and afterwards pour in the milk.
Keep stirring until the mixture becomes thick and you have a soft béchamel sauce.
Break the feta cheese into small chunks inside the pot, grate the remaining cheeses in the coarse side of the grater, and stir.
Pour in the béchamel sauce to the cheese mixture, add the egg, nutmeg, parsley and pepper, stir gently until all ingredients are well-incorporated and remove from heat.
Unroll the puff pastry sheet and spread the above mixture on top, leaving a margin from the sides so the sheet won’t be overflowing.