In a medium bowl, combine parmesan cheese, goat cheese and two egg whites. Beat with a hand mixer on high speed until smooth.
Divide galette dough into 6 sections (recipe below). On a floured surface, roll each section into a 10-inch round. Spread a generous spoonful of the cheese mixture onto each round, leaving a 1-inch border.
Trim asparagus stalks to about 3 to 4 inches long. Reserve remaining parts for other use. Arrange 5-6 asparagus stalks on each galette. Fold galette dough inwards in an overlapping fashion, leaving center exposed.
Transfer to parchment paper-lined baking sheets. Brush exposed dough liberally with egg white. Sprinkle galettes with coarse sea salt.
Bake for 35-45 minutes, until crust is golden brown. Gently place an egg yolk on each galette and bake another 3-4 minutes until yolk is set.
Make the Galette Dough:
Prepare your galette dough using these instructions. Alternatively, you can use your own two crust pie recipe or a store-bought pie dough. Let dough chill for at least three hours, ideally overnight.
Galette dough is best made the night before, which will dramatically cut down on prep time the day of your meal!