Preheat oven to 350.
In a small bowl, combine eggs, vanilla extract, vanilla beans, lime zest and lime juice. Whisk together.
In the bowl of your electric mixed, combine flour, sugar, baking powder and salt. Mix until combined. Add butter and mix until batter starts to come together. Add half of the egg mixture and mix on medium for 30 seconds. Add the remaining egg mixture in two parts, scraping down the sides of the bowl and mixing on medium speed for about 30-45 seconds each.
Cut a piece of parchment paper to fit in the bottom of your loaf pan and butter it. Spray the entire loaf pan with baking spray and lay the parchment paper down, buttered side up. Pour the batter in the loaf pan and bake for 50-55 minutes. If cake gets too brown on top, lightly tent it with foil. Let cool before glazing.