Heat the oven to 400°F. Beat the egg and water in a small bowl with a fork.
Sprinkle the work surface with the flour. Unfold 1 pastry sheet on the floured surface. Roll the pastry sheet into a 9x12-inch rectangle. Cut the rectangle into 12 (3-inch) squares. Repeat with the remaining pastry sheet, making 24 squares in all.
Stir the cream cheese, shredded cheese, garlic and bacon in a medium bowl. Spoon about 2 teaspoons cheese mixture into each pepper half.
Place 1 filled pepper half diagonally, cheese-side down, onto each pastry square. Fold the pastry up over the pepper and press firmly to seal. Brush the filled pastries with the egg mixture. Sprinkle with additional shredded cheese, if desired. Place the pastries onto 2 baking sheets.
Bake for 20 minutes or until the pastries are golden brown. Let the pastries cool on the baking sheets on wire racks for 10 minutes.