Preheat oven to 400 degrees F (200 degrees C).

Divide pastry dough into four equal portions and roll each one out in a square shape. Set pastry aside to rest.

Place a large skillet over medium heat. Add butter or margarine and allow to melt. Add onion and saute for 5 minutes, until translucent and beginning to brown. Add carrot, turnip, potato, mushrooms, and water. Lower heat and cover skillet. Allow mixture to cook for 10 minutes, stirring occasionally.

In a small bowl, dissolve yeast extract in milk. Whisk in 1 egg. Stir this mixture into cooked vegetables. Continue to stir until mixture thickens. Add cheese, and salt and pepper to taste. Set aside to cool.

Place 1/4 of filling on one half of each pastry square. Fold pastry diagonally and seal edges. Brush tops of pastry with beaten egg.

Place pasties on a baking sheet and bake in preheated oven for 30 minutes, until pastry is golden brown.