Unfold one sheet of puff pastry onto a clean surface. Cut along the line folds with a sharp knife to create 3 strips. Cut each strip into 4 equal pieces. Repeat with the remaining puff pastry sheet. Place the squares on a parchment paper-lined baking sheet and refrigerate.
Melt the butter in a large oven-proof skillet with high sides over medium heat. Add the mushrooms, shallot, garlic, salt, and pepper. Sauté 8 minutes or until the mushrooms are browned and tender. Add the sherry and simmer 2 minutes.
Meanwhile, whisk together the chicken broth, milk, and flour. Pour the broth mixture into the skillet and add the herbs. Bring the mixture to a simmer and cook, stirring frequently, 5 minutes, or until thickened. Stir in the turkey and green beans. Season with salt and pepper to taste if needed.
Let the filling cool slightly while the oven preheats to 400°F.
Remove the puff pastry squares from the refrigerator and arrange in a single layer over the filling. (I make a concentric circle in a shingled pattern.) If you have any squares leftover, leave them on the baking sheet; they can be baked to serve with the pot pie.
Whisk together the egg yolk and 1 ½ teaspoons water. Carefully brush the egg wash on the puff pastry squares (including any leftover).
Bake the pot pie for 40 to 45 minutes, or until the pastry is puffed and golden, shielding with aluminum foil during the last 10 minutes of baking if the top is becoming too browned. (Bake any remaining puff pastry squares at 400°F for 15 to 20 minutes or until browned and puffed.)
Garnish the pot pie with additional herbs, if desired, and serve with the extra puff pastry squares. Serve right from the skillet.