Preheat the oven to 325 degrees. In a stand mixer with the whisk attachment, combine the eggs, lemon zest, and sugar on medium speed. Reduce the speed to low and add the olive oil in a slow and steady stream. In a separate mixing bowl, combine the dry ingredients. Add the dry ingredients to the egg mixture in three additions, whisking at low speed the entire time. Whisk just until the batter is smooth and the ingredients have combined.
Rub a nonstick 10-inch cake pan with a film of olive oil. Pour the batter into the pan and bake for 45-55 minutes or until a cake tester or toothpick comes out dry. Remove the cake from the oven and let rest for 10-20 minutes before removing it from the cake pan.