Toast the pecans first. Spread them in a single layer in a dry skillet over medium heat and stir them every 30 seconds for 3 to 4 minutes, until they smell nutty and have darkened slightly. Pour them onto a plate and let them cool completely before adding them to the tart.

Make the shortbread crust. Whisk together the flour, powdered sugar, and fine salt in a bowl. Add the cold butter cubes and work them in with your fingertips until the mixture looks like damp sand with no dry streaks. Add the egg yolk and 1 tablespoon of ice water and stir until the dough just clumps together when you press a bit between your fingers. If it seems dry, add another teaspoon of water.

Press the dough evenly into the bottom and up the sides of a 9-inch tart pan with a removable bottom. Use the flat bottom of a measuring cup to smooth the base and your fingers to press the sides up to the rim. Freeze the crust for 20 minutes while you preheat the oven to 375 degrees F.

Blind bake the crust. Press a piece of parchment paper into the frozen crust and fill it with pie weights or dried beans. Bake for 15 minutes, then carefully remove the parchment and weights. Return the crust to the oven for 5 more minutes until the bottom looks set and just barely golden. Set it aside to cool slightly and reduce the oven temperature to 325 degrees F.

Make the caramel filling. Combine the dark brown sugar, heavy cream, and 4 tablespoons of butter in a medium heavy-bottomed saucepan over medium heat. Stir constantly until the butter melts and the sugar dissolves, about 4 minutes. Remove from heat and let it cool for 10 minutes so the eggs do not scramble when added.

Whisk the 2 whole eggs, vanilla extract, and fine salt into the cooled caramel mixture until fully combined and smooth. The filling should look glossy and uniform with no streaks of egg.

Arrange the toasted pecans in an even layer across the bottom of the par-baked crust. Pour the caramel filling over the pecans slowly. Some pecans will float up and that is fine. Place the tart pan on a rimmed baking sheet for easier handling.

Bake at 325 degrees F for 25 to 28 minutes. The edges of the filling should look set and slightly puffed, and the center should have only a slight jiggle when you gently shake the pan, similar to a set custard. Do not overbake or the filling will crack.

Let the tart cool completely on a wire rack, at least 2 hours, before removing it from the pan. Once fully cooled and set, sprinkle the flaky sea salt evenly over the top. Slice with a sharp knife and serve at room temperature.