Preheat oven to 400°F. Place four ramekins (12 oz. each) on a rimmed baking sheet lined with aluminum foil or parchment paper; set aside.  Stir together egg and water with a fork; set aside.

Unfold thawed puff pastry onto a floured surface and, working quickly, roll out slightly to make a 10-inch square. Cut out four circles of pastry to fit the top of the ramekins using the outer edge of a ramekin as a guide.  Place the circles on a lightly floured baking sheet and refrigerate while preparing the filling.

Meanwhile, melt butter in a 6-qt. Dutch oven over medium heat. Add carrots, onion, salt, and pepper and cook 4 minutes, stirring constantly, until onion is softened.

Stir in flour coating the vegetables evenly. Gradually add stock, stirring until smooth between additions. Bring to a boil over high heat. Add potatoes and thyme, reduce heat to medium-high, and simmer 12 to 15 minutes until stock is thick enough to coat the back of a spoon. Stir in beef, peas, and vinegar and remove from heat.

Ladle filling evenly amongst ramekins, then top each with a pastry circle. Cut small slits on top for venting. Brush egg wash over pastry and sprinkle with pepper, if desired. Bake 25 minutes or until the pastry is golden brown and the filling is bubbling. Let stand 10 minutes before serving.