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, combine the flour, powdered sugar, and salt. Add the softened butter and mix until crumbly. Press the mixture evenly into the bottom of the prepared baking dish to form the crust. Bake for 15 minutes or until lightly golden.

While the crust is baking, prepare the filling. In a large bowl, whisk together the eggs, granulated sugar, lime zest, lime juice, baking powder, and vanilla extract until well combined.

Once the crust is done baking, 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 to set. Cut into squares and dust with additional powdered sugar before serving.