Preheat oven to 425 degrees F. Line two large baking sheets with parchment paper. Unfold one sheet of puff pastry on a lightly floured surface. Using a pastry wheel or a sharp knife, cut sheet into nine squares (about 3x3 inches each); cut each square in half to make a total of 18 rectangles. Place rectangles about 1 inch apart on prepared baking sheets.
Bake in preheated oven for 12 to 15 minutes or until golden. Carefully remove from baking sheet; cool on a wire rack. Repeat with remaining sheet of puff pastry.
For filling, combine cream cheese, mustard, Worcestershire sauce, and green onion or chives. Fold in cooked shrimp, carrot, and bacon. To assemble, use tines of a fork to separate each pastry in half horizontally. Spread a rounded tablespoon of filling on the bottom portion of each pastry; replace top layer. Makes 36 appetizers.