Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a medium bowl, combine the softened cream cheese, sour cream, minced garlic, salt, black pepper, and crushed red pepper flakes. Mix until smooth.
Fold in the chopped spinach, chopped artichoke hearts, shredded mozzarella, and grated Parmesan cheese until well combined.
On a lightly floured surface, roll out the thawed puff pastry sheet into a 12×12 inch square.
Spread the spinach and artichoke mixture evenly over the puff pastry, leaving a 1/2-inch border around the edges.
Starting from one edge, carefully roll the puff pastry sheet into a tight log.
Using a sharp knife, slice the log into 12 equal pinwheels, about 1 inch thick.
Place the pinwheels cut side up on the prepared baking sheet, spacing them about 1 inch apart.
Bake in the preheated oven for 18-20 minutes, or until the puff pastry is golden brown and cooked through.
Remove from the oven and let cool for 5 minutes before serving.