Line a sheet pan with parchment paper and spread Prosciutto out in a single layer on top. Transfer to the oven and bake until crisp, about 7- 10 minutes (depending on thickness; take it out as soon as it looks dry / crisp.)
Whisk together egg and water. Set aside.
Unfold both sheets of puff pastry out on a clean counter or cutting board.
Brush the entire surface of the puff pastry with whisked egg (you may not need all of it). Top with cheese, thyme leaves, and a single layer of crisp Prosciutto, leaving about ½ inch free along the top edge of the pastry.
Roll the puff pastry up into a log, enclosing the filling. Pinch closed at the end. If the pastry doesn’t feel cool to the touch, refrigerate the log for 5-10 minutes.
Line two sheet pans with fresh parchment paper or silicone baking sheets .
Slice the pastry logs into quarter-inch rounds (about 20 rounds from each log). Spread them out on prepared baking sheets, leaving about 2 inches of space between each. Gently reshape the pinwheels into circles if needed.
Bake 15-18 minutes, until golden brown.
Let cool on the sheet pan for 5 minutes before transferring to a cooling rack to cool completely. Garnish with a few extra thyme leaves and enjoy!