Pulse 2 1/2 cups flour, chilled butter pieces, and salt in a food processor until mixture resembles coarse crumbs, about 10 pulses. Stir together ice-cold water and cider vinegar in a small bowl. Pour half the ice water mixture into the flour mixture; pulse to combine, about 3 pulses. Pour remaining ice water mixture in a thin stream through the opening in the lid, adding just enough to moisten and pulsing just until the mixture looks crumbly and starts to cling together.

Turn out dough onto a work surface and pat into a circle; divide in half. Form each half into a disc; wrap each disc in plastic wrap. Chill at least 30 minutes.

Preheat oven to 350°F (180°C).

Turn chilled dough out onto a lightly floured surface. Roll dough to 2 (12-inch) rounds. Trace around a 6-inch plate to get 5 (6-inch) rounds total, rerolling scraps as needed. Transfer dough rounds to 5 (4- to 4 1/2-inch) pie pans, lightly pressing into pans. Crimp edges as desired. Arrange pecan halves in the bottom of each crust. Transfer pie pans to a baking sheet.

Whisk together sugar, the 2 tablespoons flour, and nutmeg in a medium bowl. Whisk in eggs, corn syrup, the 1/2 cup water, melted butter, and vanilla until smooth. Stir in chopped pecans. Divide mixture evenly among pie crusts.