To make the crust: Combine the flour, powdered sugar, salt, & vanilla in a large bowl. Cut in the cold butter & work with your fingers until the mixture resembles cornmeal. Press into a greased 13x9" pan and bake for 18-20 minutes, or until golden.
Meanwhile make the filling: Whisk together the sugar & flour in a bowl. Add the eggs, one at a time, whisking well after each addition. Add the zest, lime juice & enough green food coloring to produce desired color (a little goes a long way.) Mix until everything is smooth & combined.
Pour filling over hot crust and return to oven to bake for an additional 18-20 minutes. When done, the filling will no longer jiggle. Let cool completely in the pan before slicing and dusting with powdered sugar. For best results, keep refrigerated & serve cold.