01 - In a medium bowl, beat together cream cheese, sugar, and vanilla extract until completely smooth and creamy. Gently fold in diced strawberries and strawberry jam until just combined. Transfer filling to refrigerator to chill while preparing dough.
02 - In a separate mixing bowl, whisk together flour, sugar, and salt until well blended. Cut cold butter into the dry mixture using a pastry blender or fingers until it resembles coarse crumbs. Gradually drizzle in cold water while mixing until a smooth, pliable dough forms. Wrap dough and refrigerate for 15 minutes to rest.
03 - Lightly dust a clean work surface with flour. Roll chilled dough to approximately 1/8 inch thickness. Using a round cutter or bowl, cut out 8 circles approximately 5 inches in diameter. Gather scraps, re-roll, and cut additional circles as needed.
04 - Place a generous tablespoon of chilled cheesecake filling in the center of each dough circle, leaving a 1/2 inch border. Lightly brush edges with beaten egg. Fold dough over filling to create a half-moon shape and press edges firmly together. Crimp sealed edges with a fork tines to ensure proper closure.
05 - Heat vegetable oil in a deep fryer or heavy-bottomed pot to 350°F. Carefully lower 2-3 pies into hot oil and fry for 2-3 minutes per side until golden brown and crispy. Using a slotted spoon, transfer fried pies to paper towels to drain excess oil. Repeat with remaining pies.
06 - Allow pies to cool for 5 minutes until safe to handle. Generously dust tops with powdered sugar while still slightly warm. Serve immediately for best texture and flavor.