Preheat the oven to 350°F (180°C). Line a 9x9 inch pan with parchment paper
In a food processor, blend together the softened butter, flour, lime zest, sugar, and salt until it creates a soft dough. Press this mixture firmly into the pan.
Bake it for approximately 20-22 minutes until ever so lightly browned and just baked through.
In a separate bowl, whisk together the flour and the sugar for the lime layer until well combined. Add the eggs, zest, lime juice, and salt, and whisk until smooth. Carefully pour the mixture of the baked base and place it back in the oven.
Bake for around 17-20 minutes until the lime layer has set. Giving the pan a little shake should show no real wobble left to the lime layer.
Once baked, cool the lime slice to room temperature, then refrigerate for at least an hour before slicing. Powdered sugar can be dusted over the top at the time of serving.