Turkey Pot Pie for Another Day

Name: Turkey Pot Pie for Another Day
Ingredients: 4 cups shredded turkey breast; 5 tablespoons good quality olive oil, divided; 1 tablespoon finely minced shallot; Zest from one lemon, preferably organic; 2 tablespoons chopped flat-leaf Italian parsely; 1 tablespoon unsalted butter; 8 ounces fresh cremini mushrooms, coarsely chopped; 2 leeks, white and pale green parts thinly sliced; 2 carrots, cut into a small dice; 1 teaspoon dried thyme; 1/3 cup dry white vermouth; 1/3 cup flour; 4 cups chicken broth or stock; 1/4 cup heavy cream or half-and-half; 3/4 cup frozen peas; 1 sheet of puff pastry, thawed; 1 egg, lightly beaten