Whip the eggs with the sugar: Transfer the sugar, the salt and the lemon zest to a bowl and mix to combine. Transfer the eggs to the bowl of your electric mixer and beat with the whisk attachment until frothy. Add the sugar mixture gradually and continue beating until the mixture thickens and resembles shaving foam (about 10 minutes).
Add the oil: While beating, add the oil in a thin stream and then add the vanilla extract.
Prepare the flour: Transfer the flour and the baking powder to a bowl and mix well.
Add the flour and the juice: Sift approximately one third of the flour over the egg mixture and fold gently with a spatula (at this tage it's OK if the flour is not completely incorporated). Add half of the orange juice and fold it again with the spatula. Continue with half of the remaining flour, then the rest of the orange juice and then the rest of the flour.
Bake: Transfer the cake batter to the bundt pan and bake for 60-70 minutes or until a toothpick inserted in the center of the cake comes out clean. Let it cool for 5 minutes, then unmold to a cooling rack and let it cool completely.
Make the lemon glaze: Transfer the icing sugar, the lemon zest and the lemon juice to a small bowl and mix well with a spoon. The glaze should be very thick if you want it to be white. If the glaze is too thick, add half a teaspoon of lemon juice at a time until it reaches the desired consistency. Spoon the glaze over the cake (you may not need it all) and let it set for 30 minutes. Serve.
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