Start by preheating your oven to 350°F. Unfold the puff pastry and divide it into three sections for smaller baking pans. Place parchment paper and weights in the center to keep the middle flat while baking.
While the pastry bakes, mix ricotta, mozzarella, parmesan, eggs, nutmeg, garlic powder, oregano, and salt and pepper in a bowl until smooth. This creamy base will perfectly hold the zucchini rosettes.
Microwave the zucchini ribbons for 30 seconds to make them pliable. Roll one or two slices into a small tube, slice in half, and carefully place on the pastry over the cheese. Repeat until the surface is covered.
Spritz a little olive oil over the top and bake for 50 minutes. The puff pastry should be golden and flaky, while the cheese filling stays creamy and the zucchini rosettes tender. Serve warm for the best taste.