Combine chestnuts, 3/4 cup of sugar, vanilla bean paste, and sea salt in a saucepan and cover with 2 inches of water.
Bring water to a boil and then turn down to a simmer. Simmer for 45 minutes, stirring occasionally.
Remove chestnuts from heat and allow to cool.
In a metal bowl combine chocolate, 3/4 cup of sugar, and olive oil. Place metal bowl on top of a pan with water that is just barely simmering.
Continuously mix the chocolate mixture until the chocolate is completely melted.
Remove metal bowl from heat and allow chocolate mixture to cool to a luke warm temperature.
Then mix in egg yolks and flour until well combined.
After that, mix in egg whites that have been beaten stiffly. Mix well.
Pour batter into a greased spring form pan with removable bottom.
Drain chestnuts and gently place them across the top of the cake.
Bake cake on the center rack of a preheated 350 degrees Fahrenheit oven for approximately 45 minutes or until a toothpick inserted into the center of the cake comes out clean.
Cool cake on cooling rack for 5 minutes and then remove it from the spring form pan. Cool cake for an additional 20 minutes. Slice and serve.