Preheat the oven to 420°F and prepare a baking sheet by lining it with parchment paper. Slice the guava paste into ¼-inch thick segments and set them aside. In a small bowl, beat the egg until well mixed.

Unfold one sheet of puff pastry directly onto the lined baking tray. Arrange the guava slices in three horizontal rows, ensuring approximately a ½-inch border of pastry remains uncovered around each row.

Moisten the exposed borders around the guava rows with a small amount of water to aid in sealing. Drape the second puff pastry sheet evenly over the guava-topped layer. Use a sharp knife or pizza cutter to divide the layered pastry into three long strips, each centered over a guava row.

Gently separate these three strips and press the edges together, sealing them by pinching with your fingers or crimping with a fork. Next, cut across the strips perpendicularly to create nine individual pastries, each revealing a peek of guava at both ends.

Brush the surface of each pastry with the beaten egg. Transfer the baking sheet to the oven and bake for approximately 22 minutes, or until the pastries are puffed and deeply golden.

As the pastries bake, prepare a simple syrup by combining 3 tablespoons of water with 3 tablespoons of sugar in a microwave-safe cup. Heat for one minute or until the sugar dissolves completely.

Upon removing the pastries from the oven, brush them immediately with the warm syrup. Allow them to cool thoroughly before gently separating them by hand or using a knife if necessary.