To make the pastry, in a large bowl, combine the flour, parmesan cheese and salt until well combined. Add the butter and cut it in with a pastry blender or your fingers until it resembles coarse crumbs the size of peas. Drizzle in 5 tablespoons of water, stirring gently with a rubber spatula until everything is evenly moistened; add the final tablespoon of water if necessary to make a cohesive dough. Shape the dough into a disk, wrap in plastic wrap, and refrigerate for at least 1 hour.

Preheat oven to 425°F. Line a baking sheet with parchment paper and set aside.

To assemble the galette, on a lightly floured work surface, roll the dough into a 12" circle about 1/4-inch thick. Carefully transfer the dough to a parchment-lined baking sheet. Brush it with olive oil and then sprinkle the center with the shredded cheeses, leaving a 2-inch wide bare strip along the edge.

Fan out the potato slices on top of the cheese, overlapping them in a mound. Break up the sausage and place on top of the potatoes. Season with salt, pepper and rosemary. Fold the edges of the dough over toward the center. Brush the edges of the crust with egg wash, and bake until golden brown and bubbly, about 25 to 30 minutes. Remove from the oven and allow to rest for about 10 minutes before slicing and serving. Enjoy!