Preheat oven to 180 °C (350 °F).
In a large bowl, combine the diced duck, shredded duck, onion, garlic, potatoes and cheese curds. Season with pepper.
In another bowl, mix the poutine gravy, beef broth and thyme.
Divide the pastry in half. On a floured surface, roll out each portion into a circle about 35 cm (14 inches) in diameter.
Line a deep baking dish with one of the rolled-out pastry circles. Pour the duck mixture into the dish and spread evenly. Add the broth mixture and fill to the rim.
Baste the edge of the pastry with the egg yolk. Cover with the other rolled-out pastry and squeeze the edges to form a seal. Trim excess pastry as needed. Baste the pastry with the egg yolk. Using a knife, make a small slit in the middle of the pastry to let steam escape.
Bake in the oven for 2 hours 15 minutes to 2 hours 30 minutes, until the pastry is golden brown.
Remove from the oven and let it rest for 15 to 20 minutes before serving.
