In a stand mixer, cream butter and sugars together until light and fluffy. Crack the egg, beat it until all one and then divide into half. Add 1⁄2 egg and vanilla extract to the cream/butter mixture and continue beating until smooth. Scrape down the sides of the bowl. Add cake flour and salt all at once in the bowl. Mix on lowest setting only until everything comes together. Don't over-mix. Remove from mixing bowl, shape into a round disk, and wrap in plastic. Let rest in refrigerator at least 30 minutes and up to overnight.
When ready to bake tart shell, preheat oven to 350°F (325°F if convection oven). Grease a 9-inch tart pan with removable bottom lightly with vegetable oil or butter. Roll out the disc of dough into a 11-12 inch round about 1⁄4" thick to fit the pan. Gently lay the tart dough inside the pan and work dough into the sides. Trim the excess off the top with a paring knife. Poke the bottom of the dough all over with a fork. Line tart shell with aluminum foil and fill with pie weights or dried beans to weigh down dough. Bake 10 minutes with beans in aluminum foil in the shell, and remove beans and bake 5 minutes longer to allow to brown a bit. Let shell cool.
In a 1 quart sized saucepan, bring sugar, corn syrup, water, and salt up to a boil while stirring every once in a while. Once boiling, cook to a dark amber color (about 340°F) without stirring. Wash down the sides of the pot with a wet pastry brush if you see sugar crystals forming on the sides of the pot. When the caramel is dark amber, immediately turn off the heat and stir in butter, heavy cream, and crëme fraiche. (Be careful to add slowly. The caramel will bubble up.) Stir until homogeneous and evenly mixed. Immediately pour caramel into tart shell. Refrigerate to cool for at least 2 hours.
In 1 quart saucepan, bring heavy cream to a boil. Put chopped chocolate in a small bowl and immediately pour in boiling cream. Let sit without stirring for about a minute. Then stir slowly to create emulsion. Pour on top of caramel layer in tart pan and evenly spread ganache around. Refrigerate at least 1 hour to set.
To serve, slice tart into 8 pieces, sprinkle each with grey sea salt and serve chilled. Enjoy!