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Ingredients

For the pastry crust:
1 1/2 cups all-purpose flour
1/2 cup sugar
1 teaspoon baking powder
1/4 teaspoon salt
1 stick (1/2 cup) cold unsalted butter, cut into 1/2-inch cubes
1 large egg
1 teaspoon vanilla

For the filling:
1/2 cup sugar
2 tablespoons all-purpose flour
1 tablespoon quick-cooking tapioca
2 lb firm-ripe large peaches (about 4), halved lengthwise, pitted, and each half cut lengthwise into fourths
1 cup blueberries (1/2 pint)
1 tablespoon fresh lemon juice

Special equipment needed:
A 9 to 9 1/2-inch (24-cm) springform pan
An electric spice grinder or blender with a 8oz mason jar
Food processor

Method

1 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.

2 Butter and dust with flour the inside of your springform pan. Press dough onto bottom and evenly (about 1/4 inch thick) about two inches up side of springform pan with floured fingertips. Chill pastry in pan until firm, about 10 minutes.

3 Put oven rack in middle position and preheat oven to 375°F.

4 Make the filling while the pastry chills. Grind 2 tablespoons sugar with flour and tapioca in grinder until tapioca is powdery. Tip: f you don't have a spice or coffee grinder, and you have a blender, you can use a 8 oz mason jar with the blender to grind the tapioca. Just put the tapioca, flour and sugar in the mason jar, unscrew the bottom (including blade) of your blender container from the container and screw it on to the top of the mason jar, with the blade pointing inside the jar. Then just invert the mason jar on to the blender base and use the blender to grind the contents. Transfer to a large bowl and stir in remaining 6 tablespoons sugar. Add peaches, blueberries, and lemon juice and gently toss to coat.

5 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.

6 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.

Note that although the cake will come out of the oven somewhat liquidy. The liquid should gel nicely as the cake cools.

Serves 8.