Pre Heat oven to 177 C/350 F/Gas mark 4. Grease and line bottom of baking pans (6, 8 or 9 inch) with parchment paper or prepare using butter and flour—doing so lightly on the sides.
Place sifter in a bowl, add in flour, baking powder, cinnamon and cardamom. Sift, whisk a couple of times to lighten and set aside.
Crack the eggs into a medium bowl, remove white bits, add rind of a lime and vanilla essence. Set aside.
In a large bowl or the bowl of an electric mixer, add butter and whisk on high for 1 minute.
Add sugar and whisk on high speed(level 2) until it is smooth, light in color, fluffy and doubled in size, about 5 minutes. Scrape down the sides and bottom mid-way.
Add eggs one at a time, and beat until combined, each time about 15 seconds. Scrape down sides as well to ensure that it is mixed evenly.
Divide the flour into 3 and add one third at a time mixing only until combined, alternating with the milk. Scrape down sides and mix gently with a spatula to combine one last time. Remove lime rind and discard.
Pour batter into the prepared pan, gently smooth the top with a spatula.
Place immediately in a preheated oven(middle rack), 350 degrees F, and bake 40-50 minutes or until golden, a skewer inserted into the center of the cake comes out clean. The center should be springy to the touch as well. Do not open the oven for the first 40 minutes.
Remove pan from the oven and let it cool for 10 mins. Invert onto a cooling rack, remove paper and flip again.