Preheat the oven to 350°F. Grease and line an 8-inch square aluminum pan with parchment paper.

In a large bowl, combine the sugar and zest the limes over it, making sure to avoid the white pith. Rub the zest into the sugar using your fingers.

Add the softened butter to the bowl and beat just to combine. Next, add the dry ingredients and beat until fully mixed. When the dough can be gathered into a ball and holds its shape when squeezed in your palm, it’s ready.

Press the dough into an even layer in the bottom of the prepared pan. Use a measuring cup or offset spatula to smooth it out.

Bake in the preheated oven for about 20 minutes, or until the edges are golden.

While the crust is baking, make the filling

In a non-reactive pot, add the sugar and zest the limes over it, rubbing the zest into the sugar with your fingers.

Juice the limes until you have the required ¾ cup and pour the juice into the pot. In a separate bowl, beat the eggs with a fork. Add the beaten eggs to the pot and whisk the mixture together until most of the egg whites are broken up.

Place the pot over medium-low heat and cook, stirring frequently with a silicone spatula, until the mixture thickens and coats the back of a spoon (it should reach 170°F on a thermometer). Remove from heat.

Slice the butter into a non-metal bowl and set a sieve over it. Pour the cooked filling through the sieve (discarding the zest and any bits of egg white). Stir the filling until the butter has melted and the mixture is smooth.

Once the crust has finished par-baking, remove it from the oven and pour the lime filling over it. Smooth the filling into an even layer.

Return the pan to the oven and bake until the sides are set, and there’s a slight jiggle in the center (about 15-20 minutes).

Let the bars cool to room temperature on the counter, then refrigerate for at least 6 hours or up to 2 days to chill and set.

Once chilled, sift a few tablespoons of powdered sugar over the bars. Slice and serve.

Store any leftovers in an airtight container in the fridge (note that the powdered sugar may dissolve, so you can add another layer of powdered sugar when you’re ready to eat the leftovers).