12slicesthinly-sliced, good-quality deli hamabout 10 ounces
2cupsfreshly grated gruyereSwiss, fontina, sharp cheddar, or similar melty cheese (about 5 ounces)
Chopped fresh parsleythyme, or chives (optional, for serving)
Lay a large piece of plastic wrap on your counter (I pressed two long sheets together at the edges to create a single larger sheet). Unfold the first sheet of puff pastry in the center of the plastic, then roll it into a 10x12-inch rectangle. Spread with 1 1/2 tablespoons mustard, leaving a 1/2-inch border on all sides. Lay 6 ham slices on top, overlapping as needed. Sprinkle with 1 cup cheese.
Starting at the long (12-inch) edge, roll the puff pastry into a log. Trim the ends so that they are even, then tightly wrap the log with the plastic wrap. Place in the refrigerator for 20 minutes. Repeat with the second sheet of puff pastry and remaining mustard, ham, and cheese. Preheat your oven to 375 degrees F and line two baking sheets with parchment paper or silicone baking mats.
Once the log has chilled, using a sharp, serrated knife, carefully cut each log into 1/2-inch-wide slices. (If each log is 12 inches, you will get 24 rolls from each one). Arrange the rolls 1 inch apart on the prepared baking sheets. Bake until the puff pastry is light golden brown and the cheese is hot and bubbly, about 18 minutes. Immediately sprinkle with chopped thyme, parsley, or chives as desired. Let cool slightly. Serve warm or at room temperature.
To make this recipe ahead: Fully bake the pinwheels, then let cool. Arrange in a flat layer on the baking sheet and freeze completely. Transfer to an airtight container and store for up to 1 month. Reheat directly from frozen on a parchment-lined baking sheet at 375 degrees F until warmed through. You could also try freezing the pinwheels unbaked, but be careful of the grated cheese coming loose. Baking the pinwheels first, then freezing, is the easiest route.
Store leftovers at room temperature for up to 3 days. Rewarm in a 375 degree F oven.