Frozen puff pastry should be left to thaw prior to using it for this recipe. Follow package instructions for thawing.
Once the puff pastry is thawed, preheat the oven to 425°F and prepare a cookie sheet with parchment paper.
Cut the puff pastry sheet into quarters and trace a 1" border along the edge with a paring knife. [See photos below.]
Prick each quarter with a fork to prevent rising.
Wash the potatoes and rosemary.
Slice the potatoes into thin circles, and mince the rosemary.
Mix the rosemary, potatoes, and olive oil in a bowl with salt and pepper to taste.
Slice the buffalo mozzarella into 1/2" rounds.
Layer each quarter of puff pastry with buffalo mozzarella slices, staying within the edges of the 1" border.
Top the buffalo mozzarella with a sprinkle of the shredded cheeses.
Layer the potato mixture on top, overlapping to create a scalloped pattern like shingles on a roof.
This is one of the few dishes in which I'd caution cooks with using too much cheese. If you use too much it will spill over the edge and you will not get that nice puff pastry border on your galette.