Lay one sheet of thawed puff pastry on a large sheet of plastic wrap. Use a rolling pin to roll it into a 10x12-inch rectangle.
Spread 1 1⁄2 tablespoons of the Dijon mustard evenly over the pastry, leaving a 1⁄2-inch border.
Layer 6 slices of deli ham on top, overlapping slightly. Sprinkle with 1 cup of the grated cheese.
Starting from a long edge, roll up the pastry tightly into a log. Trim the ends so they are even. Wrap log in plastic and refrigerate for 20 minutes.
Repeat process with second puff pastry sheet, remaining 1 1⁄2 tablespoons mustard, 6 slices ham and 1 cup cheese. Refrigerate log for 20 minutes.
Preheat oven to 375°F. Line 2 baking sheets with parchment paper.
Cut logs into 1⁄2-inch slices and place pinwheels cut-side up on the baking sheets, spaced 1-inch apart.
Bake for 18 minutes, until puffed and golden brown.
Remove from oven and immediately garnish with chopped parsley. Serve warm.