Preheat oven to 350°F. Lightly spray an 8x8-inch baking dish with nonstick cooking spray.
In a medium bowl, mix together the softened butter, flour, and granulated sugar until the mixture is crumbly but holds together when pressed.
Press the crust mixture firmly and evenly into the bottom of the prepared pan using your fingers or the bottom of a measuring cup.
Bake for 15 to 20 minutes, or until the edges are lightly golden.
While the crust is baking, in a medium bowl, whisk together the lightly beaten eggs, granulated sugar, flour, baking powder, lime juice, and lime zest until smooth.
Pour the lime filling over the hot crust as soon as the crust comes out of the oven.
Return the pan to the oven and bake for an additional 15-20 minutes, or until the filling is just set in the center and the edges are lightly golden.
Remove from oven and dust immediately with confectioners’ sugar.
Allow the bars to cool completely at room temperature, then refrigerate overnight for best texture.
Cut into squares and serve chilled.