Preheat the oven to 350°F. Grease an 8x8-inch baking dish or line it with parchment paper for easy removal.
In a medium bowl, whisk together the flour, powdered sugar, and salt.
In a separate bowl, cream the softened butter until smooth.
Gradually add the flour mixture to the butter, mixing until crumbly. Press the mixture evenly into the bottom of the prepared baking dish.
Bake the crust in the preheated oven for 15-20 minutes, or until lightly golden.
While the crust is baking, prepare the filling by whisking together the eggs, granulated sugar, lime zest, lime juice, and baking powder in a large bowl until well combined.
Once the crust is done, remove it from the oven and pour the lime filling over the hot crust.
Return to the oven and bake for an additional 20-25 minutes, or until the filling is set and slightly firm to the touch.
Allow the bars to cool completely in the baking dish on a wire rack.
Once cooled, refrigerate for at least 2 hours before cutting into squares. Dust with powdered sugar before serving.