FOR THE DOUGH: Put the flour, butter, oil, sugar, and salt in a food processor and process for about 10 seconds. Feel the dough; if it is soft enough to gather together into a ball, remove it from the bowl and form it into a ball. If it is still dry to the touch, add the tablespoon of ice water and process for another 5 or 6 seconds, then remove from the bowl and form into a ball. (The dough can be made ahead and refrigerated.)
Lightly flour a work surface and roll the ball of dough into a very thin square, no more than 1/8 inch thick. Using a round cutter with a 5-inch diameter, cut our 4 disks; or use a lid as a guide and cut out with a knife (gather up and reroll the trimmings if required). Carefully transfer the disks to a large cookie sheet lined with a nonstick baking mat, leaving a few inches of space between the disks.
Arrange the apricots and plums, alternating them in a spiral on top of each dough disk. Sprinkle the fruit with the sugar. Bake for 30 to 35 minutes, until the fruit is soft and the dough nicely browned.
Some of the juice from the fruit will have leaked out onto the cookie sheet. Before it hardens and makes the disks stick to the sheet, lift the tarts with a broad spatula and transfer them to a cooling rack or platter. Serve lukewarm or at room temperature.
Copyright © 2011 by Jacques Pépin. Used by permission of Houghton Mifflin Harcourt. All rights reserved.
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