Preheat the oven to 350 degrees F.
Spray the bottom and sides of a 9 by 13-inch cake pan with nonstick spray.
To make the crust, combine the butter and confectioners' sugar in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium-high speed for 2 to 3 minutes, until light and fluffy. Add the flour and salt, and mix another minute until well combined. Transfer the dough to the prepared pan, and pat out to an even thickness over the bottom of the pan. Bake the crust for 20 to 25 minutes, until lightly golden. Remove from the oven, and cook on a baking rack.
To make the topping, whisk together the eggs and sugar in a large mixing bowl. Add the flour, and whisk until just combined, then whisk in the lime juice and zest. Pour the lime topping over the cooled crust, then bake for an additional 25 minutes, or until the filling is set.
Allow the bars to cool completely. Generously dust with confectioners' sugar and cut into squares.
For the neatest presentation, use a metal spatula or a butcher's scraper to remove the bars from the pan. Leftovers will keep for 2 or 3 days at room temperature, or for up to a week in the refrigerator. The cookie crust dough can be prepared up to 2 days in advance, then wrapped in plastic and stored in the refrigerator. When you're ready to bake the bars, simply bring the dough to room temperature and pat out as described above.