Pasties are meat pies, or turnovers, that miners in Cornwall originally took down in the mines with them for lunch. These are appetizer-size pasties.
Cut 3-inch circles out of the pie dough. Preheat oven to 350°F.
Combine the onion, carrots, cooked beef, potatoes, flour, Worcestershire sauce, seasoning salt, and thyme in a bowl. Put a spoonful of the mixture in the middle of each dough circle.
Brush the edges of the dough circles with beaten egg, fold the dough over to make a half circle, and press the edges to seal. Use a fork to crimp the edges.
Place the pasties on a baking sheet lined with parchment paper and brush the tops with the beaten egg.
Bake for 20 to 25 minutes, until the tops are golden. Serve warm.