Mix together flour and shortening in a mixer or food processor. Drizzle in water slowly and dough will start to bind together. Once dough has formed a ball-like consistency, remove from mixer or food processor. Place dough in refrigerator and chill for one hour before rolling out dough.
Line a baking sheet with parchment paper.
Combine beef, carrots, potato, onions, garlic and seasonings.
Separate dough into 6 even pieces and form into balls. Roll out each piece of dough onto lightly floured surface. Keep others cold before rolling out each into an 8-inch circle. Divide filling evenly between the 6 pastries. Fold dough over into a half-moon shape and crimp edges of dough with fork or fingers. Cut a few small slits into each pastry to allow steaming while in the oven. Brush with egg wash and bake at 350 for an hour and fifteen minutes.