Preheat the oven to 350ºF (180°C). Spray a 9x13 inch baking pan with non-stick spray or grease with butter and line with a sheet of parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, combine room temperature butter and sugar. Beat at medium speed until light and fluffy, about 2-3 minutes.
Add eggs, one at a time and beat until just combined after adding each egg.
Add all the lemon zest, the juice of one lemon, and vanilla extract. Whisk until combined.
In a small bowl combine the flour, baking powder, and salt.
Add the dry ingredients to the bowl of the stand mixer, beat until combined.
Pour the cake batter into the pan and bake for 20 minutes or until a toothpick inserted in the center comes out clean.
Poke holes into the cake with a toothpick while it's still warm.
In a bowl combine the powdered sugar and the juice of one lemon until the powdered sugar is incorporated and the consistency is runny. Add a little bit more juice if the mixture is too dry.
Use a silicone spatula to spread the glaze on the warm cake. Let the cake rest until the glaze is set. This cake tastes even better after resting for a day at room temperature.
If you want you can decorate the cake with candied lemon slices.