To prepare crust, whisk flour and salt in a large bowl. Add butter and rub it in the flour mixture with your fingers until it resembles coarse sand.
Add 4 tablespoons of water and mix the dough together. Add more water, a tablespoon at a time, until the dough hold together when pitched.
Form a disc on a lightly floured surface. Fold the dough in half, press down to the original size and fold in half again. Repeat two more times until the dough becomes smooth.
Divide the dough into 2 pieces, in the ratio of 2/3 and 1/3, and form 2 discs. Wrap doughs with plastic wrap and refrigerate for about 30 minutes to chill.
To prepare pie filling, melt butter on medium heat in a large skillet. Add the onions and carrots, and cook until the onions are translucent, about 5 minutes.
Add the flour and cook, stirring for another minute. Slowly whisk in chicken stock to blend completely with the flour.
Add milk and cream. Decrease the heat to low and simmer for 10 minutes, stirring often. Add the chicken meat, wine, peas, corns, salt and pepper and stir well. Taste and adjust seasoning if necessary. Let cool to room temperature.
Remove the large dough from the fridge. Roll it on a floured surface, until around 3mm thick. Line a greased 9-inch pie pan with the rolled dough. Make sure you leave a tiny overhang of dough.
Roll the small dough until around 3mm thick, and cut into 12 to 14 strips, each around 1/2 inch wide.
Pour the pie filling into the prepared pie shell. Lay 6 or 7 strips over the filling, evenly spaced, and then weave with the remaining strips diagonally. Fold back the edge of the shell over the edge of the lattice strips, and crimp to secure.
Mix the egg wash ingredients, and brush the dough with the mixture. Bake at 350F for about 50 to 55 minutes, until the filling is bubbling and the crust is golden. Let cool for 5 minutes and serve.