In a large skillet, cook beef over medium heat until browned and crumbly, about 7-8 minutes. Season with salt, black pepper, and cayenne. Remove beef to a plate and wipe out the skillet.
Add butter to the skillet. When the butter melts, and the onions and cook, stirring frequently, until the onions are caramelized, 15 to 20 minutes. Stir in garlic and thyme; cook, stirring frequently, for 2 minutes. Add Worcestershire sauce; cook for 2 more minutes. Remove from heat and stir in Dijon mustard, cheddar cheese, parsley, and cooked beef.
Preheat oven to 425°F. Line a large, rimmed baking sheet with parchment paper.
Remove the pie crusts from the pouches; unroll on a lightly floured surface. Using a 3 ½-inch round cutter or bowl, cut 8 rounds from each crust (re-roll the scraps as necessary). Place half of the dough rounds on the prepared baking sheet. Brush the dough with about half of the beaten egg. Spoon a heaping tablespoon of the beef mixture on each round to within ½ inch of the edge. Top the pies with the remaining 8 dough rounds; press the edges together with a fork to seal. Freeze until firm, 5 to 10 minutes.
Use a paring knife to cut a small “X” in the top of each hand pie to vent. Brush with remaining beaten egg.
Bake until golden brown, about 17 to 19 minutes. Let the pies cool on the pan for 5-10 minutes before serving.