Thaw the puff pastry properly. Move it from the freezer to the fridge for a few hours, or leave it on the counter for 30–40 minutes until pliable but still cold. Keep it chilled to maintain flaky layers.

Toast the nuts. Warm a small skillet over medium heat. Add the nuts and toast, stirring, for 3–4 minutes until fragrant. Let them cool before blending.

Make the arugula pesto. In a food processor, combine arugula, basil (if using), Parmesan, cooled nuts, garlic, lemon juice, a pinch of salt, and black pepper. Pulse to chop. With the motor running, drizzle in olive oil until the pesto is thick but spreadable. Taste and adjust seasoning, adding a squeeze more lemon or a pinch of red pepper flakes if you like heat.

Prep the pastry. Lightly flour your work surface. Unfold the puff pastry and gently roll it into a rectangle about 10 x 12 inches. Aim for even thickness so the pinwheels bake uniformly.

Spread and layer. Spread a thin, even layer of pesto over the pastry, leaving a 1/2-inch border on one long edge. Sprinkle the shredded mozzarella or provolone over the pesto if using, and add an extra dusting of Parmesan for good measure.

Roll it up. Starting from the long edge opposite the border, roll the pastry into a tight log. Use the clean border to seal the seam. Gently pinch to close if needed.

Chill for clean slices. Wrap the log in plastic wrap and refrigerate for 20–30 minutes. This firms the butter and helps the spirals hold their shape when slicing.

Preheat the oven. Heat to 400°F (200°C). Line a baking sheet with parchment paper.

Slice the pinwheels. Unwrap the chilled log. Using a sharp knife or serrated knife, cut 1/2-inch slices. If the dough squishes, chill another 10 minutes. Arrange the slices on the baking sheet, leaving a little space between them.

Brush and bake. Brush the tops with egg wash for a glossy, golden finish. Bake for 16–20 minutes, rotating the pan halfway through, until puffed and deep golden.

Cool and serve. Let the pinwheels cool on the sheet for 5 minutes, then transfer to a rack. Serve warm or at room temperature. Finish with a tiny pinch of flaky salt and a squeeze of lemon if you like.