Place the flours, baking powder and salt in the food processor. Pulse for a few seconds. Add the butter and pulse until the butter pieces are the size of peas. Add the egg. Pulse until the dough just begins to hold together. Remove the dough and shape into a disc. Wrap in plastic and refrigerate for 30 minutes.
On a floured surface, roll out the dough and trim it to form a 28-cm (11-inch) circle. Transfer to a baking sheet and refrigerate.
With the rack in the middle position, preheat the oven to 200°C (400°F).
Salmon and mushroom filling
In a bowl, combine the salmon, lemon juice and dill. Season with salt and pepper. Let stand for 5 minutes.
Meanwhile, in a skillet over medium heat, brown the onion and mushrooms in the butter. Season with salt and pepper. Sprinkle the flour on the vegetables and stir to combine. Slowly stir in the milk. Bring to a boil, stirring constantly. Lower the heat and simmer for 1 minute. Adjust the seasoning.
Add the salmon to the mushroom sauce. Pour into a 23-cm (9-inch) pie plate. Cover with the pastry dough and crimp or press the dough to the edge of the plate. Make a hole in the centre to allow steam to escape.
Bake until the crust is lightly browned and filling is hot, about 20 minutes.