Add two tablespoons of olive oil to a heavy skillet over medium heat.
Add diced potatoes and shredded cabbage to skillet. Sautee for 5-7 mins until it begins to turn brown.
Remove from the pan and add ground beef into the pan. Cook until meat is browned, then add tomato paste, Worcestershire sauce, potatoes, cabbage, thyme, salt and pepper. Cook another 3-4 minutes over medium heat.
Add in ½ cup of water and bring to a boil. Cover and reduce heat to low for 10 mins allowing the potatoes time to become soft. Stir often to ensure that mixture does not burn.
Preheat oven to 400° F.
Once the potatoes are soft, let mixture cool a few minutes.
Cut out 3" - 5" circles of the refrigerated pie crust using a glass or biscuit cutter. Place about 1-2 tablespoons of the meat mixture on one side of the crust circles.
Fold over the circles and seal with a fork all around the half circle. Pierce the dough with the fork a few times, or cut 3 slits on the top of the pies for steam release while baking.
In a small bowl, beat the egg with 1 tablespoon of water. Using a pastry brush, brush top of each pie with the egg wash.Bake on a cookie sheet for 12-15 minutes until golden brown.