In a bowl, whisk together flour, 3 tbsp sugar, and salt. Cut in shortening until mixture resembles coarse crumbs.
Whisk egg and cold water in a separate bowl. Add to flour mixture and form dough into a ball. Wrap and chill for 30 minutes.
Preheat oven to 350°F (175°C).
Roll out half the dough to 1/8-inch thickness. Place in a 9x13-inch baking dish, covering the bottom and halfway up the sides.
Bake for 20 minutes until golden brown.
For filling: In a saucepan, combine peaches, orange juice, lemon juice, and butter. Cook until butter is melted.
Stir together sugar, cornstarch, cinnamon, and nutmeg, then add to peach mixture. Cook until thickened.
Pour filling into baked crust.
Roll remaining dough to 1/4-inch thickness. Cut into strips and weave into a lattice over the filling.
Sprinkle with 1 tbsp sugar and drizzle with melted butter.
Bake 35–40 minutes until crust is golden and filling is bubbling.