Preheat oven to 400F.
Heat a small skillet over medium heat with 2 tablespoons butter. When the butter has melted, whisk in the flour and cook for 1 minute. Whisk in the stock and milk or half-n-half and season with salt and pepper. Cook the sauce, whisking often, for a couple of minutes until is has thickened up, then stir in the Dijon and remove pan from heat. Add in the chicken, scallions, peas, carrot and dill and give it a good stir to combine everything. Set this mixture aside while you prepare your pie dough.
Grease a baking sheet lightly with butter. Lightly dust your work surface with flour and lay out the pie dough. You want it to be about the thickness of a nickel, so you may need to roll it out a bit to make it thinner. Cut the dough into eight evenly sized triangles (just like youre cutting a pie). Transfer the triangles to the baking sheet and repeat the rolling and cutting with the remaining dough.
Divide the filling among the triangles on the baking sheet leaving a little room at the edges to seal the pockets. Brush the edges of each triangle with some beaten egg and then top each triangle with the remaining wedges of dough, pressing lightly around the perimeter to seal the filling inside. If you like, you can take a fork and lightly press the very ends of the tines into the border of each pocket to give it a fancy finish.
Brush the tops of the pockets with the remaining egg wash and cut a small x in the top of each one with a paring knife or pair of scissors to let the steam escape. Bake the pockets until they're deep golden brown and crisp, about 20 minutes. Serve hot.