To make the pastry, sift the flour and salt into a large mixing bowl.
Melt the lard in the milk, bring to a boil, and pour into the flour. With a wooden spoon, mix together quickly to form a dough; it will be quite firm, somewhat like Play-Doh. Turn the dough out onto a lightly floured work surface, and knead until smooth. Cover loosely with plastic wrap, and let it rest on the work surface at room temperature for 20 minutes.
To make the filling, season the turkey and chicken all over with salt and pepper. In a large sauté pan over medium-high heat, heat 2 tablespoons of the vegetable oil. Put the turkey breast in the pan, skin- side-down, and cook until browned. Remove from the pan, and set aside. Put the chicken in the hot pan, skin-side-down, and cook until browned. Remove from the pan, and set aside along with the turkey.
Reduce the heat, and add about 2 more tablespoons of the vegetable oil to the pan, if necessary. Add the carrots, onion, and celery, and cook for about 5 minutes until softened, stirring frequently to keep from browning. Season with salt and pepper, and stir in the cloves. Add the wine, stirring to deglaze (to loosen the browned bits on the bottom of the pan), and simmer for about 5 minutes, until reduced by half. Transfer the vegetables to a bowl, and set aside to cool.
Preheat the oven to 400°F. Grease a 9-inch springform pan with vegetable shortening.
On a lightly floured work surface, roll two-thirds of the pastry into a circle about 1/4 inch thick. Line the greased pan with the pastry, allowing it to hang about 1/2 inch over the sides.
To assemble the pie, sprinkle the bottom and sides of the pastry with about one-third of the parsley, winter savory, and thyme. Line the bottom and sides of the pastry with about one-third of the bacon. Spread one-third of the vegetable mixture on top of the bacon.
Lay the turkey breast, skin-side-up, atop the vegetables. It may be necessary to trim the turkey to fit, using the trimmings to fill in any gaps. Cover the turkey with another one-third of the vegetable mixture, sprinkle on another one-third of the herbs, and cover with a thin, even layer of about another one-third of the bacon.
Arrange the chicken, skin-side-up, on top of the bacon, again trimming to fit, if necessary. Cover the chicken with the final one-third of the vegetables, herbs, and a thin, even layer of bacon.
Roll out the final one-third of the dough on a lightly floured work surface to form a circle about 9 inches in diameter. Brush the 1/2-inch overhang with beaten egg, drape the pastry circle over the top of the filled pan, and fold the 1/2-inch overhang over the edges of the pastry circle to seal together. Cut out any dough scraps to create decorative toppings, such as leaves, stars, or trees. Brush the top lightly with the beaten egg.
Set the pie on a baking sheet, and bake for 30 minutes. Cover loosely with aluminum foil, and continue baking for about another hour. Then, check the temperature every 10 minutes or so (piercing an instant-read thermometer through the crust and into the pie) until the internal temperature reaches 155°F. Remove from the oven, and set the pie on a wire rack to allow the temperature to rise to 165°F. Cool for 1 hour before carefully releasing it from the pan.
While the pie cools, make the gravy. Melt the butter in a small saucepan over medium heat. Whisk in the flour until incorporated to make a blond (light-colored) roux (thickening paste). Slowly whisk in the chicken stock and simmer for 2 to 3 minutes, until thickened. Remove from the heat, add the parsley, thyme, and sage, and allow the herbs to steep for 15 minutes. The gravy can also be prepared ahead of time and reheated just before serving.
To serve, set the cooled pie on a platter. At the table, cut a small hole in the top of the crust, and carefully pour in the hot gravy. Slice into wedges.