Heat oven to 420F. Line a baking sheet with parchment paper and cut ¼ inch thick slices of the guava paste. Add the egg to a small bowl, beat, then set aside.
Unfold the puff pastry sheet over the parchment paper.
Place the guava paste strips in three rows, leaving about ½ an inch of pastry on each side.
Brush water on the exposed puff pastry around the guava paste and them lay the remaining puff pastry over the guava paste.
Using a knife or pizza cutter cut the puff pastry into three strips with the guava pasta in the center of each strip.
Carefully slide the three strips away from each other and seal the edges using your fingertips or the tines of a fork.
Using a knife cut the pastry dough and guava paste perpendicular to the long strips, leaving you with 9 pastries. Each pastry has a little bit of guava peaking through at the ends, just like the ones available at most Cuban bakery.
Crack an egg into a small bowl and whisk it until well combined and then brush the tops of the puff pastries with the egg.
Bake at 420F for about 22 minutes or until golden brown and puffed up.
While the pastries are baking, make your simple syrup by adding 3 tablespoon of water with 3 tablespoons of white sugar to a cup and microwaving for 1 minute or until the sugar is fully dissolved.
Once out of the oven, brush the top with simple syrup and allow to cool.
Allow the pastries to cool off and then carefully rip them apart, use a knife if needed.