Thaw the puff pastry in the refrigerator for several hours or at room temperature for about 30 minutes until it's pliable but still cool. Once thawed, place the sheet on a lightly floured surface. Using a rolling pin, gently roll out the puff pastry to remove any creases and thin it slightly. Aim to shape it into a rectangle approximately 10×12 inches. I find that working while the pastry remains cool helps keep it flaky when baked.
Using a spatula, spread an even layer of softened goat cheese over the surface of the puff pastry, leaving a half-inch border free on all sides. Next, either spread the fig spread or preserves evenly on top of the goat cheese, or, if using fresh or dried figs, arrange the thin slices in a single layer over the goat cheese. Drizzle honey over the fig layer for sweetness (if desired), then scatter the chopped thyme leaves over the top. Optionally, add chopped walnuts or pecans for crunch. I love how the touch of thyme balances the richness of the goat cheese and the sweetness of the figs.
Starting from a long side, tightly roll the puff pastry and its layered filling into a log shape, keeping the roll even as you go. With a sharp knife, slice the log into about 20 even pinwheels. Arrange the slices cut-side up, ready for baking.
Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper or use a silicone mat for easy cleanup. Place the pinwheel slices cut-side up, evenly spaced, on the baking sheet. Brush each one lightly with the beaten egg to give a shiny, golden finish. Bake for 18 to 20 minutes until the pinwheels are puffed, crisp, and golden brown. I prefer to keep an eye on them in the last few minutes to avoid overbrowning.
Let the pinwheels cool slightly before serving so that the filling sets and they're easier to handle. Finish with a sprinkle of fresh thyme leaves, a light drizzle of honey, or a dusting of freshly ground black pepper for extra flavor, according to your taste. For a more elegant presentation, I like to serve these pinwheels slightly warm with an extra drizzle of honey on top.