There comes a time in every post-Thanksgiving home when leftovers are no longer interesting: The sandwiches have happened. The second-day plate with everything covered in gravy has been devoured. That’s when I gather whatever is left and make pie. Because so much of what might be included in the filling may have been salted already, make the filling first, taste it, and add more salt and pepper only if needed.
In the food processor, pulse the flour, butter, shortening, and salt until the fats are in small pieces coated with flour, about 15 times. Add the water and vodka (if using) all at once and process until the mixture almost forms a ball. Form the dough into a 3- by 4-inch rectangle using plastic wrap and a bench scraper to firmly press the dough into a cohesive form. Wrap tightly and refrigerate a minimum of 4 hours.
Remove the dough from the refrigerator and allow it to warm slightly. Roll out the crust to 11 by 15 inches and place in the slab pie pan, pressing it into the corners of the pan and allowing the excess to drape over the sides. Pierce the crust all over with the tines of a fork or a docking tool. Crimp the edge. Refrigerate.
Heat the oven to 425°F; if you have one, place a baking stone, Baking Steel, or inverted baking sheet on the center rack to heat.
Warm the olive oil in a deep, wide skillet or Dutch oven over medium-high heat until shimmering. Add the onions and cook until translucent, about 8 minutes. Add the carrots, celery, thyme, and sage. Stir well to coat the vegetables in oil and cook until slightly tender, 4 or 5 minutes. Splash in the wine and cook until the pan is nearly dry.
Over medium-high heat, add the butter and cook until foaming. Sprinkle the flour over the vegetables and cook, stirring, until the flour smell goes away and the roux (the paste created with butter and flour) has turned golden, about 4 minutes. Pour in the gravy and water and bring to a boil. Reduce the heat and let the stew bubble away until thickened, 5 or 6 minutes. Stir in the turkey and green beans. Most of these ingredients will have been seasoned already, so taste and season judiciously with salt and pepper. Cool the filling for at least 30 minutes before filling the pie.
Place a sheet of parchment in the crust-lined pie pan, weight with pie weights, and blind bake the crust (on top of the steel, stone, or baking sheet if using) for 20 minutes. Remove the paper and weights and place the pan back in the oven for 5 more minutes to dry out the crust. Reduce the oven temperature to 375°F.
Spoon the filling into the crust, smoothing the surface. Pinch off walnut-sized pieces of stuffing and dot the top of the pie. Drizzle the stuffing nuggets with the melted butter and slide the pie back into the oven. Bake until the stuffing is toasty brown and the filling is bubbling, about 25 minutes longer. Serve hot.
Swaps: Almost anything left over from Thanksgiving will find a place in the pie filling. Scatter roasted Brussels sprouts, creamed onions, or roasted sweet potatoes over the filling.