How to Make It
Make the crust In a food processor, pulse the flour with the salt to combine. Add the butter and pulse until mixture reaches a sandy consistency. With the machine running, gradually add the milk until the dough separates from the sides of the bowl. Turn the dough out onto a floured surface. Shape the dough into a disk, wrap with plastic and chill for 30-minutes to 1 hour.
Meanwhile, make your filling Preheat the oven to 400. On a rimmed baking sheet, toss the carrots, celery root, leek, Brussels sprouts and mushrooms with 1/4 cup of oil. Season with salt and pepper and spread in an even layer. Bake until the vegetables are starting to brown, but not completely tender, about 15 minutes.
In a medium enameled cast iron casserole, melt the 1 stick of butter. Gradually whisk in the flour until combined and cook over moderate heat, whisking constantly, until the mixture is the consistency of wet sand – this is the start of a roux. Continue whisking frequently until the roux is golden brown and has a toasted aroma, about 5 minutes. Be careful not to scorch.
Slowly whisk in the chicken stock and cook over medium heat until the mixture is creamy and thickened. Season with salt and pepper. Add more stock if needed and then whisk in the heavy cream. Add the chicken, roast vegetables, lemon juice and herbs to and remove from the heat. Season with salt and pepper and let cool slightly, at least 15 minutes.
On a lightly floured surface, divide the dough into 6 equal pieces. Using a lightly floured rolling pin, roll the dough to between 1/4 and 1/8-inch thickness and about 1/2-inch wider in diameter than your serving bowls. If not using immediately, stack between layers of parchment in between on a half-sheet tray, cover with plastic and refrigerate until ready to use.
In a small bowl, whisk the egg with the milk. To assemble the potpies, divide the filling between 6 bowls. Brush the egg wash around the edge of each pastry round and place the pastry rounds egg wash side down on top of the bowls. Carefully fold the edges over the sides of the bowls to seal. The pastry should have no cracks or tears, nor sag or touch the filling. Brush the tops of the pastry with more egg wash. Transfer the bowls to a rimmed baking sheet and back for about 20 minutes, or until the crust is risen and golden-brown. Remove from the oven and let rest 5-10 minutes before serving.