Let the frozen puff pastry thaw at room temperature until softened, about 30 minutes.
Meanwhile, preheat the oven to 400ºF (200ºC). Line a baking sheet with parchment paper.
Crack the egg into a small bowl or cup. Add 1 tablespoon (15 mL) water, and whisk until blended. In another small bowl, mix together the cheeses.
Unfold the thawed puff pastry sheet and place on a lightly floured work surface. Using a pastry brush, brush some of the egg mixture evenly over the dough. Sprinkle half of the cheese mixture evenly over half of the egg-brushed dough.
Fold the uncovered dough over the cheese and press gently to seal. Brush the top with the egg mixture, sprinkle with half of the remaining cheese mixture, and press gently to help stick. Turn the dough over, brush the other side with the egg mixture, sprinkle with the remaining cheese, and press gently. Discard any remaining egg mixture.
Cut the pastry lengthwise into 4 equal strips. Holding each strip by the ends, turn the ends a few times in opposite direction to make a twist. Place the twists, evenly spaced, on the baking sheet.
Bake until browned, about 10 minutes. Let cool briefly. Serve warm or at room temperature.