This summery dessert was inspired by an unforgettable galette that Deborah Madison, a well-known chef and author and a great advocate of farmers' markets, made many years ago for dinner before a performance by the Sante Fe Opera.
1 3/4 cups unbleached all-purpose flour
1 teaspoon salt
1/2 cup (1/4 pound) plus 2 tablespoons chilled unsalted butter, cut into small pieces
2 tablespoons chilled solid vegetable shortening
4 to 5 tablespoons ice water
1 1/2 pounds plums
3 tablespoons sugar
1/2 vanilla bean
, split lengthwise
2 tablespoons whole milk, or half-and-half
To make the pastry dough, sift together the flour and salt into a bowl. Add the butter and shortening and, using a pastry blender, 2 knives, or your fingers, work the fat into the flour until the mixture has the consistency of coarse cornmeal.
Add the ice water 1 tablespoon at a time, stirring and tossing with a fork until the dough forms a shaggy mass. Turn the mass out onto a floured work surface and knead the dough a few times with the heel of your hand until the clumps of dough come together. Shape into a disk, wrap tightly in plastic wrap, and refrigerate for 1 hour before rolling out.
To make the filling, while the dough rests, working over a large bowl, cut the plums into quarters, discarding the pits. Sprinkle with the sugar. Using the tip of a knife, scrape the seeds from the vanilla bean into the bowl. Stir to mix everything together.
Preheat the oven to 375°F. Place a pizza stone near the work surface where you will be rolling out the dough.
Remove the dough from the refrigerator. Hit the dough a few times with the rolling pin, giving it a quarter turn each time you strike it, to soften it slightly. On a lightly floured work surface, roll out the dough into a 15-inch round. Cut away the ragged edges. Wrap the dough over the rolling pin and carefully transfer the pastry round to the pizza stone, laying it out flat. Arrange the plums, cut side up, on the center of the round in an overlapping spiral 10 inches in diameter. Loosely gather the dough and arrange over the edge of the fruit. Make sure there are no holes in the pastry (pat away any cracks) or the juices will run out. Brush the dough with the milk or half-and-half.
Bake the galette until the crust is golden brown and the filling is bubbing, about 1 hour. Carefully remove the pizza stone from the oven and allow the tart to rest on the stone for 30 minutes. Use the removeable bottom of a tart pan to transfer the cooled tart to a flat serving plate. Serve warm or at room temperature.