Preheat oven to 350F and line an 8x8 inch pan with parchment. Start a pot of gently boiling water (for your double boiler) on the stove.
Mix together shortbread ingredients until thoroughly combined and press down into a baking pan, pressing it up against the sides (this will help keep the filling in place). Prick with a fork, and parbake for 20 minutes. Crust should be puffy but not golden.
Whisk filling ingredients in a glass or metal bowl. Cook filling over the double boiler, continuously whisking until the filling thickens and reaches a temperature of 170F (about 18 minutes). Make sure the water isn't hitting the bottom of the bowl, as it could curdled your filling (if it is, reduce the heat or remove some of the water).
Strain filling through a sieve to remove lemon zest.
Pour hot filling into hot crust and bake until filling is just set, about 10 minutes. It should have a slight jiggle.
Cool completely and slice into 9 pieces. Keep refrigerated for 2-3 days.
Notes
If you want to freeze your lemon bars, simple space them out on a parchment lined baking tray or plate (whatever you can fit into your freezer) and freeze for 2-3 hours. Then transfer to a sealable container. Freezes up to 1 month.