1 1/2 cups all-purpose flour
1/2 cup sugar
1 tsp baking powder
1/4 tsp salt
1/2 cup cold unsalted butter, cut into 1/2-inch cubes
1 large egg
1 tsp vanilla
1/2 cup sugar
2 Tbsp all-purpose flour
1 Tbsp quick-cooking tapioca
4 firm-ripe large peaches, pitted and cut into eighths
1 cup blueberries (1/2 pint)
1 Tbsp fresh lemon juice
For the pastry
Grease and flour a 9-inch springform pan.
Pulse together flour, sugar, baking powder, and salt in a food processor until combined. Add butter and pulse just until mixture resembles coarse meal with some small (roughly pea-size) butter lumps. Add egg and vanilla and pulse just until dough clumps and begins to form a ball, about 15 pulses.
Press dough onto bottom and evenly (about 1/4 inch thick) all the way up side of springform pan with floured fingertips. Chill pastry in pan until firm, about 10 minutes.
Put oven rack in middle position and preheat oven to 375 degrees F.
For the filling
Grind 2 tablespoons sugar with flour and tapioca in grinder until tapioca is powdery, then transfer to a large bowl and stir in remaining 6 tablespoons sugar. Add peaches, blueberries, and lemon juice and gently toss to coat. Spoon filling into pastry and bake, loosely covered with a sheet of foil, until filling is bubbling in center and crust is golden, about 1 3/4 hours.
Transfer cake in pan to a rack and cool, uncovered, 20 minutes, then carefully remove side of pan.
Cool cake to barely warm or room temperature, then cut into thick wedges with a sharp knife before serving.
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