Mix 2 1/2 cups flour, 1 tbsp. sugar, and 1 1/2 tsp. salt in a large bowl. Drop in 7 tbsp. butter and the shortening. Using your hands, a fork, a pastry blender, or two knives, work butter and shortening into the flour mixture until it resembles cornmeal with some pea-size pieces.
Using a fork, quickly stir in 1/2 cup very cold water. Turn chunks of dough and crumbs onto a clean surface. Knead just until dough starts to hold together, 5 to 10 times. Divide dough in half and pat each half into a 6-in. disk. Wrap in plastic wrap and chill 15 minutes or up to overnight.
Put an oven rack on the lowest rung. Preheat oven to 375°. Unwrap one disk of dough and put on a floured surface. Roll into a 12-in. circle (about 1/8-in. thick), turning 90° after each pass of the rolling pin to keep it from sticking. Transfer to a 9-in. pie pan, letting the dough fall into place (if you push or stretch it into place, it will shrink back when baked). Trim dough edges to 1/4 in. past rim of pie pan. Cover with plastic wrap and chill 15 minutes. Meanwhile, roll out second disk into an 11-in. circle. Cut into ten 1-in.-wide strips. Transfer to a baking sheet, cover with plastic wrap, and chill 15 minutes.
While crusts chill, mix remaining flour, 1/4 cup granulated sugar, the brown sugar, tapioca, remaining salt, the cinnamon, pepper, nutmeg, and cloves in a bowl. Add blueberries and lemon juice; toss. Taste and add more granulated sugar (up to 1/4 cup), if you like. Pour berry mixture into crust and dot with remaining butter.
To weave a lattice crust, lay 5 strips of pie dough vertically across pie, spacing evenly. Take the top of every other strip and fold it back halfway. Lay a strip horizontally across center of pie, next to folds of vertical strips. Unfold vertical strips back over horizontal strip. Fold back vertical strips that were left flat last time, and repeat with a second horizontal strip, placing it above first strip (away from you). Repeat with a third horizontal strip above second. Repeat this process on lower half of pie, using remaining 2 strips of dough.
Fold bottom crust edge up over top crust and crimp edges together. Bake until crust is browned and filling is bubbling in the center, 60 to 75 minutes. Cover edge with strips of foil if browning too quickly. Let cool until bottom of pie pan is room temperature.
Note: Nutritional analysis is per serving.