Preheat the oven to 170C. Butter & flour a 9x5 loaf tin; set aside.
In a medium bowl, whisk together the flour & the baking powder. Set aside.
In a large bowl, whisk together the sugar & the lime zest, ensuring the zest is evenly dispersed. Add the eggs, yogurt, & melted butter to the sugar and whisk until thoroughly combined.
Add the flour mix to the egg mixture & stir until just combined.
Transfer the mixture to the prepared loaf tin & bake in the preheated oven for 45-50 minutes, or until the loaf is golden brown and a skewer inserted into the centre of the cake comes out clean. Leave the cake to cool in the tin for 10-minutes, before transferring to a wire rack to cool completely.
To make the glaze, in a small bowl, use a fork to combine the icing sugar and lime juice - using more lime juice for a runnier glaze. When the cake is cooled, use an offset spatula or spoon to spread the glaze evenly over the top.