- With the rack in the middle position, preheat the oven to 200°C (400°F). Line a 30 x 43-cm (12 x 17-inch) cookie sheet with parchment paper.
- Roll out each package of puff pastry into a 13 x 40-cm (5 x 16-inch) rectangle. Transfer both to the cookie sheet and cover with a sheet of parchment paper. Place another cookie sheet on top. Bake for 30 minutes. Remove from the oven. Remove the top cookie sheet and sheet of parchment paper and turn the pastry over. Return to the oven and bake, uncovered, for 10 minutes. Let cool.
- Trim the edges of the pastry to even them out and obtain 2 identical rectangles. (This also makes the separate layers of pastry more visible.) Set aside.
- With the tip of a knife, split the vanilla bean lengthwise. Scoop out the tiny seeds. In a saucepan, gently heat the milk and the vanilla seeds and pod. (If using vanilla extract, do not add it now.)
- In a bowl, combine the sugar, flour and cornstarch. Add the eggs, whisking until the mixture is smooth. Slowly whisk in the hot milk and vanilla bean. Return the mixture to the saucepan. Bring to a boil over medium heat, whisking constantly and scraping the bottom and corners of the saucepan to prevent sticking. Reduce the heat and simmer for about 1 minute. Remove the vanilla pod. (If using vanilla extract, add it after removing pastry cream from the heat.) To keep a skin from forming, lay a piece of plastic wrap directly on the surface of the hot cream. Let cool. Refrigerate until well chilled, about 3 hours.
- Lower the oven temperature to 190°C (375°F). Line a 40 x 43-cm (12 x 17-inch) cookie sheet with parchment paper.
- In a saucepan over medium heat, bring the milk, butter, sugar and salt to a boil. Remove from the heat. Add the flour all at once. Stir vigorously with a wooden spoon until the dough forms a smooth ball that pulls away from the sides of the
- Return the saucepan to the stove and cook over low heat while stirring the dough for about 2 minutes.
- Remove from the heat and let cool for a few minutes. Add the eggs, one at a time, beating vigorously with a wooden spoon after each addition until smooth (if you prefer, the eggs can be incorporated using an electric mixer or food processor).
- Fit a pastry bag with a 1-cm (1/2-inch) plain tip and fill it with the dough. Pipe 30 balls, each about 3 cm (1 1/4 inches) in diameter, onto the cookie sheet. Bake for 20 minutes. Lower the oven temperature to 170°C (325°F) and continue baking to dry out the puffs, about 20 minutes. Remove from the oven and let cool. With the tip of a knife, cut a slit for filling in the bottom of each ball. Set aside.
- In a bowl, whip the cream with sugar and vanilla extract until it forms firm peaks. Set aside 375 ml (1 1/2 cups) of the whipped cream.
- Whisk the remaining whipped cream into the chilled pastry cream. Refrigerate.
- Partially fill a sink with cold water. In a saucepan, bring 60 ml (1/4 cup) water and the sugar to a boil over medium heat. Cook without stirring until the syrup turns golden brown (do not let it turn dark). Remove the saucepan from the heat and set it in the sink of cold water to stop the cooking. When the caramel thickens slightly but is still fluid, remove the saucepan from water.
- (Be careful when doing the following step because hot caramel can cause severe burns. To be extra safe, wear latex gloves.)
- Spear the bottom of a choux pastry ball on a fork and dip it in the caramel to coat the top. Set the ball on the cookie sheet, caramel side up, and let cool. Repeat for the remaining balls. If you prefer, you can use tongs instead of a fork.
- Fit a pastry bag with a small plain tip and fill with half the pastry cream mixture. Fill the choux pastry balls through the slit in the bottom. You will need about 23 balls for assembly.
- Place a puff pastry rectangle on a rectangular serving platter. Cover the top with the remaining pastry cream mixture. Set the second puff pastry rectangle on top of the cream. Spread the remaining whipped cream on top. Arrange 16 of the choux pastry balls, dipped side up, in 2 side-by-side rows (8 balls per row) on the whipped cream. Place the remaining 7 balls in a single row on top.