Preheat the oven to 375°F (190°C). Use a 9-inch deep-dish pie plate with a capacity of at least 1½ quarts (6 cups), and set it on a rimmed baking sheet.
Gently roll and fit one pie crust into the bottom and sides of the plate without stretching the dough. Chill the fitted shell for 30 minutes; keep the second crust refrigerated until needed.
Line the chilled shell with parchment and fill it about two-thirds full with pie weights or dried beans. Bake for about 20 minutes, until the crust is partially set and no longer looks wet or raw. Time varies with the crust and pan; continue briefly if needed without fully browning it. Carefully lift out the parchment and weights.
Reduce the oven to 350°F (175°C). Measure 4½ cups of well-drained peach slices (about 1 kg/2¼ lb, usually from four 15-ounce cans). Gently combine the peaches with both sugars, vanilla, cinnamon, nutmeg, and lemon zest in a large bowl.
Mix 1 tablespoon cornstarch with 2 tablespoons cold water until smooth, then fold the slurry into the fruit. Do not add the canned peach liquid; this filling goes into the crust without a stovetop simmer.
Spoon the filling into the partially baked shell, keeping it below the rim.
Cut the second crust into strips and arrange them across the filling in a rustic lattice. Rest the strip ends on the rim; do not try to seal raw dough to the partially baked crust.
Brush the lattice with the ¼ cup melted butter.
Bake at 350°F for approximately 45–60 minutes, until the lattice is golden and cooked through and the filling bubbles through the lattice near the center. Continue baking as needed. Shield the edges or loosely tent the top with foil if they brown too quickly.
Rest for 20–30 minutes before serving so the juices can settle. The filling will be juicy and spoonable.
Serve warm with ice cream or whipped cream if desired. Refrigerate leftovers within 2 hours and use within 3 days.