Preheat oven to 425 degrees F.
In a medium bowl, combine the flour with the salt and seasoning choices. Set aside.
In a large saucepan, combine the milk and the butter. Bring to a boil over high heat.
Remove the pan from the heat when the butter melts and add the seasoned flour all at once.
With a wooden spoon, stir vigorously just until the dough masses into a ball and does not cling to the sides of the pan.
Transfer the dough to a large mixer bowl.
On medium speed, beat in the eggs, one at a time. Stir after each addition until the egg is completely absorbed. Continue this process until 5 of the eggs have been used. The dough should be smooth and satiny.
Add the cheeses to the dough and beat in thoroughly.
Spoon 2 teaspoons of dough about 1" in diameter onto parchment lined baking sheets, setting the gougeres about 1-1/2" apart. Beat the remaining egg and, with a pastry brush, lightly brush the tops to glaze.
Bake for 10 minutes, rotating the baking sheets halfway through, until the gougeres reach a rich golden brown. Let cool slightly. Serve immediately.