In a medium bowl, mix together the turkey, 2 tablespoons of olive oil, shallots, lemon zest, and parsley; set aside.
Melt 1 tablespoon of butter with 1 tablespoon of olive oil in a dutch oven. Sauté the mushrooms over medium-high heat until cooked through and lightly browned; transfer to a bowl, and set aside.
Heat 2 tablespoons of olive oil over medium heat in a clean dutch oven; add leeks, carrots, and thyme and cook until vegetables begin to soften (about 8 minutes). Raise the heat slightly, add the dry vermouth, and cook until most of the liquid has evaporated.
Add flour to the carrot mixture, stirring constantly for about 1 minute. Whisk in the stock and cream, then simmer until the sauce thickens (about 10 minutes); remove from heat and allow to cool to room temperature.
Mix the cooled sauce with the lemon-parsley turkey, mushrooms, and frozen peas; divide the mixture between 4 mini-loaf pans.
Cut 4 pieces of puff pastry large enough to cover each loaf pan with 1/2 inch hanging over on each side. Crimp the edges with the tines of a fork to seal.
Preheat oven to 400° F. Brush the tops of frozen pies with egg and bake for 35 - 40 minutes, or until the tops are golden brown. Let stand for 5 minutes before serving.