Put an oven rack on the lowest rung and preheat oven to 375°. Lightly dust your counter and rolling pin with flour, then unwrap one disk of dough. With short strokes from center outward, roll dough into a 12-in. circle (about 1/8 in. thick), turning 90° after every 3 or 4 passes of the rolling pin to keep it from sticking. Transfer dough to a 9-in. pie pan, letting it fall into place (if you push or stretch the dough, it will shrink back when baked). Trim overhang to 1/4 in. Cover with plastic wrap and refrigerate at least 15 minutes and up to overnight. Meanwhile, roll second disk into an 11-in. circle. Transfer to a baking sheet, cover with plastic wrap, and refrigerate at least 15 minutes and up to overnight.
While crusts chill, put berries in a large bowl. Sprinkle with flour, 1/4 cup granulated sugar, brown sugar, tapioca, lemon juice, and salt. Stir gently until berries are well coated. Taste and add more granulated sugar if you like.
Pour berry mixture into chilled bottom crust and dot with butter. Unwrap top crust and lay over pie. Fold bottom crust edge up over edge of top crust and crimp edges together. Cut several vents in top crust and sprinkle with remaining 1 tsp. sugar. Put pie on a rimmed baking sheet and bake until crust is browned and filling is bubbling, 60 to 75 minutes. (Cover edges with foil if they become too dark before middle of top is nicely browned.)
Let pie cool until bottom of pie pan reaches room temperature, at least 3 hours. Serve with whipped cream or ice cream if you like.
Note: Nutritional analysis is per serving.