Make the Crust:
In a medium bowl, whisk together the flour and salt. Add the butter and using your fingers or a pastry cutter, mix the butter into the flour until it resembles parmesan cheese or wet sand. It’s ok if there are some larger butter pieces in there. Pour in the milk and stir the mixture together using a fork until dough forms. Do not overwork the dough. Dump the dough out onto a lightly floured surface and divide into two equal pieces. Shape each into a 6-inch disk, wrap in plastic wrap and refrigerate until ready to use (at least an hour). If you’re in a hurry, place them in the freezer for 20-30 minutes.
Make the Filling:
Heat a large skillet over medium-high heat, melt butter and then add the onions and carrots. Season with half of the salt and cook until onions are translucent, 3-5 minutes. Add in the garlic, thyme, rosemary, sage and lemon zest and cook until fragrant, 1 minute. Sprinkle 3 Tbsp. flour over vegetables and cook, stirring constantly, until flour begins to stick to the bottom of the pan, about 30 seconds. Add the sherry and lemon juice and cook, stirring constantly, about 1 minute. Add the milk, shredded chicken, peas, corn, and remaining salt and bring to a simmer. Cook, stirring occasionally until everything is warmed through, about 5 minutes. Taste and adjust seasoning as needed. Transfer mixture to a shallow platter to cool completely before filling the pie crust.
Assemble the pie:
Preheat oven to 350 degrees. On a lightly floured surface, roll out one of the dough discs into a 12 inch round and place in a 9-inch deep dish pie plate. Pour the chicken filling inside the pie plate and place in fridge while you roll out the other dough disc into a 12 inch round. Place the second pie crust on top of the chicken filling, pinch the edges of the two doughs together to seal and then crimp the edge. Brush the entire top with egg wash (egg + 1 tsp. water) and make a few slits in the pie dough for ventilation. Place the pie plate on a sheet tray (this catches any juices) and bake for about 55-65 minutes, until the juices are bubbling and the crust is golden brown. If your crust seems to be browning too quickly before the pie is done, simply cover it with aluminum foil.
Allow pie to cool for about 10 minutes before serving.