Prepare the shortbread crust.

Cream together softened butter and powdered sugar.

Sift flour, sugar, and salt.

Add dry ingredients to the butter mixture and blend.

Add vanilla extract and blend.

Wrap the dough in wax paper and chill for 4-6 hours in the refrigerator.

Press the dough into two 9-inch tart pans.

Bake at 325 degrees F for 27-30 minutes.

Prepare the lemon butter filling.

Combine lemon zest and sugar in a food processor and process until fine.

In a bowl, whisk together eggs, sugar, and zest mixture.

Stir in freshly squeezed lemon juice.

Place the bowl over a saucepan of simmering water and stir until the mixture thickens.

Stir in butter, a piece at a time, until melted and smooth.

Strain the filling through a fine-mesh sieve.

Pour the lemon butter into the tart shells.

Let cool completely before serving.

Dust the edges of the tarts with powdered sugar before serving.