Pulse flour, confectioners' sugar, and a pinch of salt in a food processor to combine. Add butter, and process until the mixture resembles coarse meal, about 10 seconds. With processor running, add cold water, 1 tablespoon at a time, until a dough forms (do not process more than 20 seconds). Cut dough in half; shape each half into a disk. Wrap in plastic wrap; refrigerate at least 30 minutes, or up to 1 day. Cut 1 disk into 12 pieces; on a lightly floured work surface, flatten each piece into a 2-inch round. Press a round onto bottom and up sides of each cup of a 12-cup nonstick mini-muffin tin. Repeat with remaining disk of dough and second muffin tin. Refrigerate 30 minutes. Preheat oven to 400 degrees F. Stir together granulated sugar, cornstarch, lemon juice and zest, and a pinch of salt in a medium bowl. Add berries; toss to coat. Fill shells with berry mixture. Bake until crusts are brown and filling is bubbling, about 25 minutes. Let cool slightly in tins. Run a knife around tarts; remove from tins. Let cool completely on rack.