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.
Add the chopped spinach, chopped artichoke hearts, shredded mozzarella, and grated Parmesan to the cream cheese mixture. Stir 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 into a tight log, sealing the edge by pressing gently.
Using a sharp knife, slice the log into 12 equal pinwheels, about 1-inch thick each.
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 slightly before serving.