Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper to ensure easy cleanup.
Prepare the homemade pesto sauce: In a food processor, combine the fresh basil leaves, grated Parmesan cheese, extra virgin olive oil, pine nuts, and garlic cloves. Pulse until the mixture is smooth and well-blended. Season with salt and pepper to taste.
Roll out the thawed puff pastry sheets on a lightly floured surface. Spread a generous layer of pesto sauce evenly over the pastry, leaving a small border around the edges.
Fold the pastry sheet in half over the pesto. Use a rolling pin to gently press and seal the edges.
Using a sharp knife or a pizza cutter, slice the folded pastry into strips approximately 1 inch wide. Twist each strip gently to create a spiral effect.
Place the twisted pastry strips onto the prepared baking sheet. Brush the tops with the beaten egg to achieve a golden hue during baking.
Sprinkle the lightly toasted pine nuts over the pastry twists for added crunch and flavor.
Bake in the preheated oven for 15-20 minutes, or until the pastry is pīŋ and golden brown. Keep an eye on them to avoid overbaking.
Allow the pastries to cool slightly before serving, as this will enhance their crispiness.