Combine the flour, salt, baking powder and sugar and in the bowl of a food processor (or just use a mixing bowl if doing by hand).
Add half of the chunks of butter and pulse until mixture is coarse. Add remaining butter and pulse just until it is broken up with some larger pea size chunks here and there.Add vinegar to the mixture and pulse to mix, then add half the water and pulse. Add the remaining water a tablespoon at time until mixture holds together when you pinch it. Most likely you will use it all.
Empty onto a pastry mat and pat into one big mass. Divide in half and wrap halves separately. Chill for at least and hour or until ready to use.
Chicken
Place the chicken breasts on a baking sheet and rub them with olive oil. Sprinkle generously with salt and pepper. Roast at 350 degrees F for 35 to 40 minutes, or until cooked through. Set aside until cool enough to handle, then remove the meat from the bones and discard the skin. Cut the chicken into large dice. You will have 4 to 6 cups of cubed chicken.
Filling
In a small saucepan, heat the chicken stock along with the bouillion. In a large pot or Dutch oven, melt the butter over medium heat and saute the onions for 10 to 15 minutes, until translucent. Add the flour and cook over low heat, stirring constantly, for 2 minutes. Gradually stir the hot chicken stock into the flour mixture. Simmer over low heat for 1 more minute,stirring, until thick.
Lastly, add the heavy cream, cubed chicken, carrots, peas or green beans, pearl onions and parsley. Taste and add salt and pepper as needed.
Assembly
Preheat the oven to 375 degrees F. Divide the filling equally among 4 ovenproof bowls. Divide the dough into quarters and roll each piece into an 8-inch circle. Brush the outside edges of each bowl with the egg wash, then place the dough on top. Trim the circle to ½-inch larger than the top of the bowl. Crimp the dough to fold over the side, pressing it to make it stick. Brush the dough with egg wash and make 3 slits in the top. Sprinkle with sea salt and cracked pepper.
Place pies on a baking sheet and bake for 1 hour, or until the tops are golden brown and the filling is bubbling hot. Makes 4 giant servings
Notes
If you want to use a different kind of cooked chicken or already cooked chicken, you will need about 5 cups.