Step 1: Wash and trim the rhubarb stalks, discarding any leaves. Chop the rhubarb into small, 1/4 to 1/2-inch pieces. In a medium saucepan, combine the chopped rhubarb, granulated sugar, lemon juice, and 1/4 tsp of vanilla extract. Stir well.
Step 2: Cook the rhubarb mixture over medium heat, stirring occasionally, for 8-10 minutes, or until the rhubarb has softened and the liquid has thickened slightly. It should resemble a chunky compote. Remove from heat and let cool completely.
Step 3: In a medium bowl, beat the softened cream cheese with powdered sugar and the remaining 1/4 tsp of vanilla extract until smooth and creamy. Use an electric mixer for the best results.
Step 4: Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper. Lightly flour a clean work surface. Unroll one sheet of thawed puff pastry.
Step 5: Using a sharp knife or a pizza cutter, cut the puff pastry sheet into 9 equal squares (3 rows of 3). Repeat with the second sheet of puff pastry, yielding 18 squares in total. Place these squares on the prepared baking sheet, leaving some space between them.
Step 6: In the center of each puff pastry square, dollop about 1 tablespoon of the cream cheese mixture. Spread it gently, leaving a 1/2-inch border around the edges. Then, spoon about 1 tablespoon of the cooled rhubarb compote over the cream cheese layer.
Step 7: In a small bowl, whisk the egg with 1 teaspoon of water to create an egg wash. Brush the edges of each puff pastry square with the egg wash.
Step 8: Fold each square into a triangle by bringing one corner to the opposite corner and pressing the edges to seal. You can use the tines of a fork to crimp and seal the edges firmly.
Step 9: Bake the rhubarb cream cheese puff pastries for 15-20 minutes, or until the pastry is golden brown and beautifully puffed. The exact time may vary depending on your oven. Keep an eye on them after 12 minutes.
Step 10: Carefully transfer the baked pastries to a wire rack to cool slightly. While still warm, you can dust them with a little powdered sugar for an extra touch of sweetness and presentation. Serve warm or at room temperature.