In a large bowl, whisk together the flour, powdered sugar, and salt. Add the cold, cubed butter. Use a pastry blender or your fingers to cut the butter into the flour until the mixture resembles coarse crumbs. Slowly add the ice water, one tablespoon at a time, mixing until the dough just comes together. Be careful not to overmix!
Form the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes. This chilling time is crucial to prevent the crust from shrinking during baking.
On a lightly floured surface, roll out the chilled dough into a circle that's about 12 inches in diameter. Carefully transfer the dough to a 9-inch tart pan with a removable bottom. Gently press the dough into the bottom and up the sides of the pan. Trim any excess dough from the edges.
Prick the bottom of the crust with a fork (this prevents it from puffing up). Line the crust with parchment paper and fill it with pie weights or dried beans. This is called blind baking.
Bake in a preheated oven at 375°F (190°C) for 20 minutes. Then, remove the parchment paper and pie weights and bake for another 5-10 minutes, or until the crust is lightly golden brown. Let the crust cool completely.
In a medium saucepan, combine the granulated sugar and water. Cook over medium heat, without stirring, until the sugar dissolves and the mixture turns a deep amber color. This will take about 5-7 minutes. Watch it carefully to prevent burning!
Remove the saucepan from the heat and carefully whisk in the butter until it's completely melted. Then, slowly pour in the heavy cream (it will bubble up). Stir until smooth.
Return the saucepan to low heat and cook for another 1-2 minutes, stirring constantly, until the caramel is smooth and glossy. Remove from heat and stir in the sea salt. Taste and add more salt, if desired.
Pour the warm caramel filling into the cooled tart crust. Spread it evenly.
Refrigerate the salted caramel tart for at least 2-3 hours, or until the caramel is set. This allows the caramel to firm up enough to slice cleanly.