Let the butter cool, then whisk in 2 tablespoons of lemon juice.
Bake at 350 for 30 minutes until the edges just start to turn golden. The middle will still VERY gooey, but the cake is definitely done at this point. Allow to cool completely.
Meanwhile, make the lemon glaze. Melt 1 tablespoon of butter and whisk into powdered sugar. Add the zest of 1 lemon, and just enough lemon juice to make a thick, but pourable glaze, about 1½ - 2 tablespoons. Whisk until smooth and combined.
Pour glaze over shortbread and allow to set before cutting into bars.
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