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

Transfer frozen puff pastry onto a piece of parchment paper. While puff pastry is still nearly frozen, use a 2 ¼-inch round cookie cutter to cut out circles of dough. Transfer cut circles onto the prepared baking sheet.

Once as many circles are cut as possible, stack up 2 or 3 pieces of trimmings together and roll between parchment paper to the original thickness; punch out more circles. Again, chill dough in freezer as needed.

Making sure dough is still very cold and firm, use a smaller 1 ½-inch round cookie cutter to punch out a circle in the center of each dough circle. Do not remove the center piece, but carefully push it back into place.

Bake in the preheated oven until pastry is light golden brown and puffed, about 20 minutes. Let cool for 5 minutes. Flip each popper over, and generously grate Parmesan on the bottom of each one, covering completely. Flip back over, trapping cheese underneath. Use a teaspoon to firmly press down the center circle of pastry dough, leaving the outside ring of pastry untouched.

Bake in the preheated oven for 7 minutes. Remove and let cool for about 10 minutes before topping.

Fill the center of each popper with a generous tablespoon of pizza sauce. Top with mozzarella cheese. Place 1 slice of pepperoni on each and press down lightly with your finger.

Bake until the edges of pepperoni and cheese start to brown, about 20 minutes.

Transfer onto a cooling rack and let cool to warm or room temperature before serving, about 10 minutes.