2Transfer the boiled limes to a bowl and add sugar, milk, eggs, neutral oil, vanilla bean paste, and salt. Use an immersion blender to combine the ingredients.
3Sift in the flour and baking powder and mix until combined.
4Pour the batter into a loaf pan.
5Bake at 325F.
6Whisk together powdered sugar, lime juice, and water to create the icing and pour it over the cooled cake.