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.

Preheat the oven to 350 degrees F (175 degrees C). Roll out 1/2 of the chilled dough to 1/8-inch thickness.

Place in a 9x13-inch baking dish, covering the bottom and halfway up the sides. Bake in the preheated oven until golden brown, about 20 minutes.

Mix peaches, orange juice, and lemon juice in a large saucepan. Add butter and cook over medium-low heat until butter is melted.

Stir together sugar, cornstarch, cinnamon, and nutmeg in a bowl; mix into peach mixture until combined. Pour into baked crust.

Roll remaining dough to 1/4-inch thickness. Cut into 1/2-inch-wide strips.

Weave strips into a lattice over peaches. Sprinkle with 1 tablespoon sugar, then drizzle with melted butter.