Pick through all olives making sure not pits are left behind. Puree all ingredients in a food processor. Keep refrigerated for up to a month.
In a stand mixer fitted with the whisk attachment, beat eggs, brown sugar and salt on hight speed until light and fluffy; about 3 minutes. Continue beating adding olive oil in thin stream. Add wine, and the sifted powders, on low speed. Transfer cake batter into a large clean container. Meanwhile, coat olives and ham with a tablespoon/10g of flour; fold olives mixture into the batter along with the tapenade. Fill up greased mold and bake.
Coat olives and ham with flour. It prevents them from sinking into the bottom when baking.
Bake at 400ºF/205ºC for 15 minutes. Lower the heat to 350ºF/180ºC and continue baking for 25 minutes more. Top cake with cheese and place under the broiler until it melts. Serve at room temperature. Refrigerated savory cake for up to 5 days. Enjoy!