Preheat oven to 400ºF. Remove one puff pastry sheet from the freezer and let warm up for 30 minutes at room temperature. Line a baking sheet with parchment paper. You'll want to work on the parchment paper.

When the puffy pastry is pliable — when it can bend without cracking — center the pastry on the parchment paper and unfold. Puff pastry is usually slightly rectangular; place the longer side horizontal to you (so that the longer sides are at the top and bottom from your POV).

Distribute the stuffing over fig jam, leaving a 1 inch clear space at the top edge. (This will help keep the stuffing from leaking out of the side of the roll.)

Sprinkle the grated cheese over the stuffing.

Starting with the bottom edge of the pastry (i.e., the edge closest to you), roll the pastry from bottom to top into a long a roll. Use the parchment paper to lift and help roll the pastry when necessary. Recenter the roll on the parchment paper, with the seam underneath the roll.

Bring the top and bottom edges of the parchment paper up together and lift the roll evenly, transferring it to the freezer. Take care to not let the roll bend and crack as you're moving it. Leave the roll in the freezer for 10 minutes (this will make cutting easier).

After 10 minutes, transfer the roll back to the baking sheet. Use a very sharp knife to cut 1-inch slices from the roll, wiping the knife clean between cuts. You'll get 8 or 9 slices from the roll.

Arrange the slices on the parchment paper, about an inch apart.

Brush the tops and sides of the pinwheel slices with the egg wash.

Bake for 15 minutes or until the pastry is golden.