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. 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.