Preheat the oven to 325°F. Grease pan and dust with 1 TBSP flour, turning pan to coat all sides and edges. Set aside.
In the bowl of the mixer, add the butter and beat until light yellow, about five minutes. Add the sugar and beat on high speed for 5 more minutes until you get a creamy mixture.
Reduce the mixer speed to half, and add the eggs, one by one. Before adding each egg, the previous one must be fully integrated into the mixture.
Add the flour little by little, alternately with the milk. That is, add a little milk, then another little flour, and so on until the flour is fully integrated.
Then add vanilla, the baking powder, with the lime juice, and the lime zest. Mix until fully incorporated. Be careful not to beat for more than two minutes after adding the baking powder.
Pour the mixture into the pan that was previously prepared.
Bake for approximately 55 to 60 minutes. When the surface of the cake looks golden, open the oven and test if the cake is ready by inserting a toothpick into the cake. If it comes out dry, remove the pan from the oven, turn it off and let it cool at room temperature.
After about 2 hours, overturn the cake onto a plate.
Whisk the ingredients for the glaze together in a small mixing bowl. Drizzle over cooled cake & top with additional lime zest.