Step 1

Make filling: Melt butter in a large saucepan over medium- high heat. Add onion, garlic, celery, carrots, and coriander. Season with salt and pepper. Cook, stirring occasionally, until onions are translucent, 8 to 10 minutes. Stir in potatoes and Brussels sprouts. Cook until vegetables are tender and beginning to brown, 6 to 7 minutes. Transfer to a bowl. Reserve saucepan.

Step 2

Make cream sauce: Melt butter in reserved saucepan over medium heat. Add flour and cook, whisking, until a smooth paste forms, about 30 seconds. Reduce heat to medium-low and whisk in stock, heavy cream, and thyme. Cook, stirring occasionally, until thickened slightly, 8 to 10 minutes. Stir in peas and lemon zest; remove from heat. Stir in chicken. Add to vegetable mixture and stir to combine. Cool completely.

Step 3

Preheat oven to 400°F. Let dough sit at room temperature 10 to 15 minutes. On a floured work surface, roll one dough disk into a 14-inch round and fit into a 10-inch cast-iron skillet or deep-dish pie plate. Trim edges, leaving a 1 1/2–inch overhang. Roll second dough disk into a 12-inch round.

Step 4

Spoon filling into bottom crust. Place second round of dough over filling and trim to a 1-inch overhang. Fold edge of bottom crust over top, pressing bottom and top crusts tightly together. Ensure crust rests on edge of pan and press edge with your fingers to seal loose pleats. Cut two small vents in top; brush with egg.

Step 5

Bake until crust is golden brown and filling is bubbling, 50 to 60 minutes, shielding after 30 minutes with aluminum foil, if necessary.