In a medium saucepan heat milk, butter, salt, pepper and nutmeg. Bring to a boil over medium high heat. When butter melts reduce heat to low.
Add flour to mixture all at once. Cook over low heat, beating with a wooden spoon for 2 minutes, until mixture pulls away from the sides of the pan. Remove from heat
Dump hot mixture into bowl of a food processor fitted with steel blade.
Immediately add eggs, Gruyere, parmesan and pulse until eggs are incorporated and dough is smooth and thick.
Either spoon mixture into pastry bag and pipe or drop batter in small spoonfuls onto a lightly greased cookie sheet or a cookie sheet covered with parchment paper.
Brush tops of uncooked gougeres with egg wash.
Bake for 15 minutes, until golden brown but still soft inside. Serve hot from oven or allow to cool to room temperature.