Crust: Pulse flour, salt, and sugar in a food processor to combine. Add butter; pulse until mixture resembles coarse crumbs with some larger pieces remaining. Add ice water; pulse until dough just starts to come together. Pat dough into a disk, wrap in plastic, and refrigerate until firm, at least 1 hour or overnight.
Let dough stand at room temperature until pliable. Roll out on a lightly floured surface to an 11-inch round, about 1/8 inch thick. Fit into a 9-inch pie plate, fold over edge, then crimp. Freeze until firm, about 1 hour.
Preheat oven to 375 degrees. Line pie-crust with parchment and fill with weights or dried beans. Bake 25 minutes, then remove parchment and weights and continue to bake until golden, about 15 minutes. Let cool.
Filling: Meanwhile, bring milk, cream, and lemon basil just to a boil in a medium pot. Remove from heat, cover, and let steep at least 2 hours (or overnight in the refrigerator).
Preheat oven to 350 degrees. Return milk mixture to a simmer; remove lemon-basil sprigs. Whisk together egg yolks and sugar in a bowl, then whisk in cornstarch and salt until mixture is pale and thick, about 2 minutes. Slowly whisk in hot milk mixture until smooth. Pass mixture through a fine sieve into piecrust; skim any foam from surface with a spoon. Bake just until set in center (if browning too quickly, tent edges with foil), about 30 minutes. Let cool completely. Refrigerate until chilled, at least 4 hours or up to overnight.
Berries: Gently toss strawberries, raspberries, and elderberry clusters with sugar in a bowl. Let stand until juicy, about 5 minutes. Spoon berries and juices over chilled pie, top with lemon-basil flowers, and serve.