Put an oven rack in the middle position and preheat oven to 350°. Stir together walnuts, pecans, flour, brown sugar, and salt in a small bowl. Add butter and stir with a fork until mixture forms small clumps (break apart any large clumps with your fingers). Set aside.
Gently mix peaches, sugar, and tapioca in a large bowl. Taste and add additional sugar if you like. Set aside.
Dust your counter and rolling pin with flour. With short strokes from center outward, roll dough into a 12-in. circle (about 1/8 in. thick), turning 90° after every 3 or 4 passes of the rolling pin to keep it from sticking. Transfer dough to a 9-in. deep-dish glass pie plate, letting it fall into place (if you push or stretch the dough, it will shrink back when baked). Trim overhang to 1/2 in., tuck edge under, and crimp edge. Pile peaches into crust, then top with streusel.
Put pan on a rimmed baking sheet and bake until topping and bottom crust are well browned, about 1 hour. Let cool to room temperature, at least 2 1/2 hours, before serving.
Note: Nutritional analysis is per serving.
If your peaches are exceptionally juicy, toss with an additional tbsp. of tapioca. To peel peaches, make a small x on the bottom of the fruit, then plunge into boiling water for 30 seconds. Once cool, the skin will pull free.