Make crust: Sift together flour, 3 tablespoons sugar, and salt in a medium bowl. Work in shortening with a pastry blender until mixture resembles coarse crumbs. Whisk together egg and cold water in a small bowl. Sprinkle over flour mixture; work with hands to form dough into a ball. Wrap with plastic wrap and chill in the refrigerator for 30 minutes.
To begin, set the oven temperature to 350 degrees Fahrenheit (175 degrees Celsius).
Take half of the refrigerated dough and roll it out until it is 1/8 inch thick. Then, place the rolled-out dough in a baking dish measuring 9x13 inches, ensuring that it covers the bottom and reaches halfway up the sides.
Cook in the oven which has been preheated until it turns a golden brown color, which usually takes around 20 minutes.
Prepare the filling by combining peaches, orange juice, and lemon juice in a spacious saucepan. Heat the mixture over medium-low heat until the butter is completely melted. In a separate bowl, combine sugar, cornstarch, cinnamon, and nutmeg, and then add this mixture to the peach mixture, ensuring it is well combined. Finally, pour the resulting mixture into the pre-baked crust.
Instructions for the remaining dough involve rolling it out to a thickness of 1/4 inch and cutting it into strips that are 1/2 inch wide. These strips should then be woven into a lattice pattern over the peaches. To enhance the sweetness, sprinkle 1 tablespoon of sugar over the lattice and finish by drizzling melted butter on top.
Cook the mixture in the oven that has been preheated until the upper crust turns a golden brown color, which usually takes about 35 to 40 minutes.