Combine dry ingredients, cut into butter with mixer or by hand until crumbly. Fold in sour cream and add water. Dough will be similar to biscuit dough, wet but dry enough to handle and roll out. Let rest 10 min. On a generously floured surface, divide into six portions and roll out into thin 8-9” rounds 1/8” thick.
Sauté butter, potato and onion for 5 min. Add mushrooms and garlic and cook 2 min more. Add chicken, peas, parsley, thyme, wine, stock and cream. Reduce by 1/3 (approx. 3 min). Add Parmesan and season to taste. Divide filling among dough rounds and fold edges in toward the center, leaving middle exposed. Brush dough with beaten egg. Bake at 350 degrees for 25-30 min until golden brown. Serve immediately.