Make the pastry: Combine the flour and salt in a food processor and pulse to mix. Add the butter and pulse until the mixture resembles very coarse bread crumbs. Transfer the mixture to a large bowl.
In another bowl, whisk together the egg and sugar. Pour the egg mixture over the flour-butter mixture and mix with a fork. Squeeze a bit of the mixture between your fingers. If it holds together, transfer the dough to a lightly floured surface; if not, add a couple of teaspoons of ice water and test again. Knead gently and form into a ball, divide the pastry in half, and flatten into 2 disks. Wrap each disk in plastic and refrigerate for at least 30 minutes before using.
Make the tart: Roll out the pastry on a floured surface and line a 9-inch or 9 1/2-inch (23-cm or 24-cm) tart pan. Prick the base of the tart with a fork and refrigerate for at least 30 minutes.
Preheat the oven to 375°F (190°C).
Place the tart shell on a baking sheet. Line the tart with parchment paper and fill it with dried beans. Bake until the pastry is just set, about 15 minutes. Remove the paper and beans and continue to cook until the pastry is a dark golden color, 10 to 15 minutes. Transfer the tart to a wire rack and leave to cool completely.
Combine the sugar and butter in a deep, heavy saucepan over medium heat. Stir to mix and cook, stirring occasionally, until the butter and sugar caramelize, 10 to 15 minutes. The sugar and butter will go through several stages. First it will look like a flour-butter roux, then it will appear curdled, and then the butter will leak out of the sugar mixture. Don’t worry: It will all come together in the end.
While the caramel is cooking, pour the cream into a saucepan and bring it to a boil over medium heat. Remove from the heat and set aside.
Keep stirring the butter-sugar mixture, watching carefully as it begins to caramelize and remembering that the heat in the pan will continue to cook the caramel once it is removed from the burner. You want a rich, dark caramel color, but you don’t want to burn the mixture, which will give it a bitter taste. When the caramel reaches the right color, remove the pan from the heat and slowly and carefully pour in the cream; the mixture will bubble and spit. When the caramel stops bubbling, return it to low heat and cook for 5 minutes, stirring to dissolve the caramel in the cream. Remove the pan from the heat and let the caramel cool for 10 minutes. Slowly pour the cooled caramel into the baked pastry shell and chill the tart for at least 2 hours.
This tart is easier to cut when it is chilled. Remove the tart from the pan and, using a wet knife, cut it into wedges. Serve the tart at room temperature, however, for maximum flavor, with a dollop of whipped cream.