In a small bowl, whisk together flour, salt, baking soda, and baking powder and set aside.

Use a large mixing bowl for the wet ingredients and start with the eggs and sugar. Whisk together and, when smooth, begin to slowly pour in the olive oil while continuing to whisk the egg and sugar mixture. When smooth, set aside.

Measure out the milk and add the Cointreau, lemon zest, and lemon juice. Mix right before you’re ready to use.

Alternate adding the dry ingredients and the milk mixture to the wet ingredients. Start with half of the flour mixture, follow with the milk mixture, and finish with the rest of the flour mixture. Whisk after each addition but do not overmix.

Pour into the prepared bundt pan and bake for 45 minutes. The cake is done baking when golden brown along the edges and a long toothpick or cake tester comes out with a few crumbs.

Let the cake cool in the pan for a few minutes on a cooling rack and then turn out onto an easy-to-clean wire rack on a large piece of wax paper or parchment paper.

While the cake cools, make the glaze. Sift powdered sugar into a mixing bowl and set aside.

Slice two or three vanilla beans lengthwise and scrape the seeds from the pod. Add the vanilla bean paste to the powdered sugar. Zest two lemons and add the lemon zest to the powdered sugar. Juice the lemons you just zested into a liquid glass measuring cup and slowly add to the powdered sugar mixture as you whisk and until you get the desired consistency. The glaze should be thicker than syrup but thinner than pudding.

Let the glaze set and then slice and enjoy. This cake keeps very well for a few days, covered, at room temperature.