1. In large saucepan or Dutch oven, heat olive oil over medium heat then add the butter. When butter is melted, add the onion, carrots, celery, parsnip, and turnip. Cook, stirring occasionally, for approximately 10 minutes. Add the mushrooms, garlic, summer savory, oregano, and rosemary. Cook 2-3 minutes longer, stirring continuously. Add 1 cup chicken or turkey stock and the potatoes. Bring to a boil over high heat then reduce to low and simmer for approximately 8-10 minutes, or until vegetables start to soften. Remove from heat.
2. While vegetables are cooking start preparing the sauce by heating second amount of oil in separate saucepan over medium heat. Add the butter. Stir in the flour and cornstarch (mixed together). Whisk in the remaining 2 cups of warm chicken or turkey stock along with the whipping cream, cheeses, Dijon mustard, Worcestershire sauce, white wine, cayenne, parsley, and salt and pepper. Reduce heat slightly and cook, stirring frequently, until mixture thickens to the consistency of a very thick chowder.
3. Add the cooked chicken and frozen peas to the saucepan or Dutch oven containing the vegetables. Stir. Pour the sauce into the mixture. Stir. Remove from heat and cool for about ¾ hour at room temperature, stirring occasionally, then refrigerate until mixture is cold.

Pastry:

1. In medium-sized bowl, whisk the flour, salt, and sugar together. Cut the butter and lard into chunks and add to the flour. With a pastry cutter, cut the butter and lard into the flour until the fats resemble the size of large peas.
2. In a measuring cup, whisk the egg and vinegar together. Add enough cold water to measure 1 cup. Add the egg-vinegar-water mixture to the flour, small amounts at a time, and mix with a fork. Add only enough water that the dough clings together and can be formed into a ball.
3. Divide the dough into 20 equal pieces. Form disk shapes with each piece. Wrap disks individually in plastic wrap or place, single layer, in large airtight container. Place in the refrigerator for about 15 minutes to chill. Remove one disk at a time from the refrigerator and roll pastry to desired thickness, generally between 1/16”and 1/8” thickness. Transfer pastry to a 4” or 5” pie plate that has been lightly sprayed with cooking spray or greased. Cut off excess dough so pastry is flush with the pie plate edge. Place pie shell in refrigerator to keep chilled. Repeat with remaining disks.
4. Prepare pastry for the top crusts in the same manner as for the bottom crust. Remove pie shells from refrigerator and equally divide cold chicken filling between the prepared cold shells. Brush outside rim edges of bottom crust pastry along pie plate edge with a bit of water to moisten. Transfer rolled-out pastry to the top of pie filling in each pie plate. Trim excess pastry flush with the pie plate edge. Press the edge of the pastry all around the pie plate rim with tines of fork to adhere top crust to bottom crust. Cut slits in top of pie pastry to allow steam to escape as pie bakes. For additional venting, prick each pie in several places with tines of a fork.
5. For pastry egg wash, lightly beat the egg yolk with 1 tbsp water in a small bowl. With a pastry brush, lightly brush the pie with the egg wash.
6. Place pies in refrigerator for 30 minutes to allow filling to settle and to chill pastry to reduce shrinkage while pies bake.
7. While pies are chilling, place oven rack in lowest position in oven. Preheat oven to 425°F. Place pies on large baking sheet(s) and bake for 10 minutes then lower oven temperature to 375°F and bake for approximately 35-40 minutes or until filling is bubbling through slits in tops of pies. For unbaked frozen pies, bake at same temperatures for approximately 50-55 minutes, or until filling is bubbling through slits in tops of pies.