- In the bowl of a food processor, combine the flour and salt. Add the butter and pulse for a few seconds at a time until the butter has the size of peas. Add the water. Pulse again until the dough is just beginning to form. Add water, if needed. Remove the dough from the processor and form into two disks with the hands. Cover with plastic wrap. Refrigerate for 30 minutes.
- In a saucepan, bring the broth to a boil. Cook the chicken in the simmering broth for 10 to 15 minutes. Remove the chicken from the saucepan and let cool. Cut the chicken into cubes. Set aside.
- In the same saucepan, add the potatoes and carrots in the broth. Bring to a boil and simmer until tender. Drain. Keep the vegetables and broth separately. There should be 375 ml (1 1/2 cups) of broth. Add broth, if needed.
- In the same pan, brown the onion in the butter. Season with salt and pepper. Sprinkle the flour over the onion and cook for 1 minute, stirring constantly. Whisk in the broth. Bring to a boil, stirring. Simmer gently for about 5 minutes. Add the chicken and vegetables. Adjust the seasoning. Let cool.
- On a floured work surface, roll out the two discs of dough and line a 23-cm (9-inch) pie plate with one of the pastry sheets. Make incisions in the second sheet.
- With the rack in the lowest position, preheat the oven to 200 °C (400 °F).
- Spoon the filling into the crust. Top with the second pastry sheet. Tightly seal the edge by crushing it with a fork or your fingers. Brush with milk.
- Bake for about 35 minutes or until the crust is golden brown.