Adjust oven racks to lower and middle positions; heat oven to 350°.

For the filling: Gently toss peaches (may use five 10-ounce bags frozen peaches, thawed overnight in refrigerator, if ripe peaches are unavailable) and sugar together in large bowl; let stand for 30 minutes, tossing several times. Drain peaches in colander set over large bowl, saving drained peach juice. Whisk¼ cups drained peach juice, cornstarch, lemon juice, salt, cinnamon, and nutmeg together in small bowl; discard excess peach juice. Toss juice mixture with peaches and transfer to 8-inch-square glass baking dish.

For the topping: While peaches are macerating, combine flour, sugars (reserving 1 tablespoon granulated sugar), and salt in workbowl of food processor; drizzle vanilla over top. Pulse to combine mixture, about five 1-second pulses. Add butter and half of nuts; process until mixture clumps together into large, crumbly balls, about 30 seconds, pausing halfway through to scrape down sides of workbowl. Sprinkle remaining nuts over mixture and combine with two quick pulses. Transfer mixture to parchment-lined baking sheet and spread into even layer (mixture should break up into roughly 1/2-inch chunks with some smaller, loose bits). Bake on middle rack until chunks are lightly browned and firm, 18 to 22 minutes. (Topping can be baked ahead of time, as directed, then cooled and stored in an airtight container.)

To assemble and bake: Grasping edges of parchment paper and lifting so as to break crunble into uneven 1/2- to 3/4-inch pieces, slide topping over peaches and spread into even layer with spatula, packing down lightly and breaking up any very large pieces. Sprinkle remaining tablespoon sugar over top and place on lower rack. Increase oven temperature to 375° and bake until well browned and fruit is bubbling around edges, 25 to 35 minutes. Cool on wire rack until warm, at least 15 minutes; serve.