Make creme caramel: Preheat oven to 225 degrees F.
Spread strawberries on a baking sheet and bake in middle of oven 30 minutes to dry slightly.
Transfer baking sheet to a rack to cool strawberries.
Increase temperature to 350 degrees F.
In a dry heavy saucepan cook granulated sugar over moderately low heat, stirring slowly with a fork (to help sugar melt evenly), until melted and pale golden.
Cook caramel, without stirring, swirling pan, until deep golden.
Immediately pour caramel into a 9-inch glass pie plate, tilting plate to coat bottom and sides evenly.
Put pie plate in a baking pan.
In a saucepan heat cream just to a boil and remove pan from heat.
In a bowl whisk together egg, yolks, vanilla, and a pinch of salt until combined well and in a stream add warm cream, whisking.
Skim off any froth and carefully pour custard into pie plate.
Arrange strawberries decoratively on their sides in custard (custard should completely cover strawberries) and add enough hot water to pan to reach halfway up side of plate. Bake creme caramel in middle of oven about 40 minutes, or until custard is just set but still trembles slightly (custard will continue to set as it cools).
Remove plate from pan and cool custard completely on a rack.
Chill creme caramel, loosely covered with plastic wrap, at least 4 hours and up to 1 day.
Make crust: In a large bowl with fingertips or a pastry blender blend together flour, brown sugar, salt, and butter until mixture resembles coarse meal.
Add 1 tablespoon ice water and toss mixture with a fork until incorporated.
Add some or all of remaining ice water, 1/2 tablespoon at a time, tossing with fork to incorporate until mixture just begins to form a dough.
On a work surface with heel of hand smear dough in 3 or 4 forward motions to help distribute butter.
Form dough into a ball and flatten to form a disk. Chill dough, wrapped in plastic wrap, 1 hour.
On a lightly floured surface roll out dough into a 10-inch round (about 1/8 inch thick) and transfer to a baking sheet.
Using a 9-inch plate as a guide, trim dough to a 9-inch round.
Prick round all over with a fork and chill 30 minutes.
Bake round in middle of oven until golden, about 30 minutes, and cool completely on baking sheet on a rack.
Just before serving, assemble tart.
Have ready a flat serving plate at least 10 inches in diameter with a slight lip.
Run a thin knife around edge of creme caramel and rotate pie plate back and forth to make sure creme caramel is loosened.
Slide crust on top of creme caramel and invert serving plate on top of crust.
Invert tart onto serving plate (caramel will run to edges of plate) and garnish with strawberries.