Preheat the oven to 375 degrees F.
Add the oil and butter to a heavy skillet over a medium setting. Cook the shallots, dill, and garlic, for about 5 minutes, until fragrant.
Add the flour and stir, cooking for about 2 minutes, until the flour is golden brown.
Pour in the wine and broth gradually, whisking as you do. Season with salt and pepper.
Bring to a boil, and then reduce heat and simmer for about 10 minutes, whisking occasionally. The mixture should thicken slightly.
Add the chopped carrots and cook for about 5 minutes. Then add the spinach and cook until tender, about another 2 minutes.
Remove the skillet from the heat, and stir in the turkey, cooked rice, and lemon juice and zest. Season with salt and pepper as desired.
Line the bottom of a 9-inch deep dish pie plate with one layer of the pie dough.
Fill the pie plate with the turkey and rice mixture.
Top with the remaining pie crust, pinching around the edges to seal.
Beat the egg, and brush it over the pie crust.
Bake in the oven about 30 to 40 minutes, until the crust is golden brown and the filling is bubbling.