Makes 8 pastries

Poaching the apricots: In a 4-quart saucepan, bring 2 cups water, 1 cup sugar, and lemon juice to a boil. Add the apricots and simmer for 8 minutes. Take pan off the heat and let apricots cool in the liquid. Drain and pat apricots dry before using.

The Pastry Cream: Put the milk, 1/4 cup sugar, salt, egg yolks, and cornstarch in a 2-quart saucepan. Split vanilla bean lengthwise, scrape seeds into pan, and toss in the pod. Stir with wire whisk, bring to the boil, whisking constantly, and let the pastry cream boil for one minute. Remove from heat, scrape pastry cream into a strainer set over a bowl. Push the cream through the strainer and discard the vanilla bean. Cover with plastic wrap and a layer of ice cubes. Leave ice cubes in place until the cream cools.

The Pastry: Preheat oven to 350°F. On a lightly floured surface, roll the puff pastry to 1/4 inch thickness. Flour the edges of a 4-inch round cookie cutter and cut 8 rounds from the dough. Clean the work surface and sprinkle it generously with sugar. While you work on one round, keep the others covered with plastic wrap. Place a pastry round on the sugar and dust the top lightly with flour. Roll until it elongates to an 8-inch oval. Brush flour off the top and put the oval on an unbuttered baking sheet, sugar side up. Repeat with the remaining pieces, leaving just a little room between each pastry on the baking sheet.

Baking the Pastries: Spoon a walnut-sized dollop of pastry cream onto the center of each oval and set 2 apricot halves side by side on the cream to resemble sunny-side-up eggs. Bake about 35 minutes, until golden and beautifully puffed. While the pastries are baking, heat apricot jam and water just to the boil. Remove from heat and push through a strainer; keep warm until ready to use. As soon as the pastries are baked, transfer them to a cooling rack. Brush apricot glaze all over them, and let cool a bit before serving.