For the filling:
- Preheat oven to 375 degrees. Remove pie dough from refrigerator, and let rest at room temperature while you prepare filling.
- In medium heavy-bottomed cast-iron pan, melt 3 tablespoons butter with drizzle of oil over medium-high heat. While pan is heating, season chicken with salt and pepper. Sear meat on both sides. Set aside.
- In same pan, melt remaining butter over medium heat. Add thyme and sear potatoes, being careful to not stir them too much. Remove potatoes and add remaining vegetables and greens. Note: If pan is dry, add just enough oil to coat vegetables.
- Once vegetables are translucent and slightly softened, deglaze with wine, scraping pan bottom to get all brown bits. Once alcohol has cooked off (smell it), add potatoes and stock. Simmer until potatoes are soft. Add chicken and simmer 5 minutes. Taste and season.
- While filling is simmering, mix yolks with starch to form batter. Add 1 tablespoon simmering mixture to egg yolk/starch mixture at a time, constantly stirring so eggs do not curdle. Once mixture is warmed through, add to simmering filling slowly, again constantly stirring to prevent egg from scrambling. Once all is added, bring to boil to activate starch.
- When mixture has thickened, place in a wide, shallow pan to cool.
- While mixture cools, roll rested dough into 2 12-inch disks or 4 6-inch disks. Place in bottom of baking vessel(s), line crust with parchment and pie weights and bake 20 minutes. Remove from oven, allow to cool, and lower heat to 350 degrees.
- Fill cooled crust(s) with filling and top with second pie crust. Brush with egg wash, cut vents in top crust, and bake until top is golden brown, about 30 minutes.
For the crust :
(Note: Crust must be made at least 8 hours ahead of time.)
- Mix 1 cup plus 2 tablespoons flour with salt in bowl of stand mixer fitted with paddle attachment. Mix on medium-low (setting 3 on a KitchenAid mixer) and slowly add in butter. When butter is the size of peas, turn mixer off and add remaining 1¼ cups flour. Mix on low just to combine.
- Add water in a slow, steady stream and mix until dough comes together and is just barely sticky. Note that you may not need all the water.
- Form dough into a disk and wrap tightly in plastic. Refrigerate for at least 8 hours (and up to 3 days) or freeze for up to 3 months.
Yield: 2 (12-inch) pie crusts or 4 (6-inch) crusts