TO PREPARE CAKE
Preheat oven to 350°F.
In a large bowl, zest the 3 lemons and mix zest into the sugar.
Supreme the zested lemons using a thin knife to cut out only the flesh and then cut each segment into 1/4-inch pieces and reserve. [Editor’s note: Helpful instructions on how to “supreme” citrus may be found online.] Squeeze the remaining membranes and other lemon parts to produce roughly 1/4 cup of juice. Add the buttermilk to the juice and mix until incorporated. Pour the buttermilk mixture into the sugar with zest and mix until well incorporated. Whisk in eggs and olive oil.
In a separate bowl, mix together all the dry ingredients then fold the dry ingredients into wet mixture. Next, gently fold in the lemon segments.
Spray a loaf, Bundt or 9- by 9-inch cake pan with non-stick cooking spray.
Place batter into prepared baking dish. Note: Batter should go no more than about halfway up the side of the dish.
Bake for 50–55 minutes or until golden brown (actual time will depend on size and depth of baking pan) and a knife inserted into the center comes out clean. When done, remove from the oven and allow to cool on a rack for 10–15 minutes before removing from the pan.
To serve, glaze the completely cooled cake with vanilla sugar and allow time for it to set up before cutting into the cake.
TO PREPARE SIMPLE VANILLA SUGAR GLAZE:
Stir together sugar and milk until smooth then beat in corn syrup and vanilla extract until glaze is smooth and glossy. If glaze is too thick, add more corn syrup.
Note: You may also simply dust the cooled cake with confectioner’s sugar rather than glazing.