Preheat oven to 375 degrees.
Spray 10-inch fluted tart pan with removable bottom with non-stick spray. Mix cookie crumbs and butter until moist clumps form. Press dough over bottom and up sides of pan. Bake about 10 minutes. Cool completely.
Whisk nectar, sugar and cornstarch in saucepan until smooth. Add half of peaches and lemon juice. Mash to a coarse puree. Simmer until mixture is thick, stirring constantly. Cool completely. Fold in remaining peaches. Spread filling evenly over crust.
Arrange blackberries around top edge of tart. Refrigerate at least 4 to 6 hours. Serve at room temperature.
Adapted from Bon Appétit.