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Preheat the oven to 350° Fahrenheit. Line a baking sheet with parchment paper.
Zest all 3 lemons, then juice 2 of them. Set aside.
Batter
Beat the softened butter and sugar with an electric mixer until light and fluffy in a large bowl.
Mix in vanilla extract, lemon zest, and 1 tablespoon lemon juice.
Add the eggs to the batter - one at a time.
Sift the flour into a separate bowl and add the baking powder.
Gradually add the flour into the batter and beat until well combined.
Bake
Spread the batter evenly on the prepared baking sheet. Bake at 350° Fahrenheit on the middle rack for about 20 minutes, or until a toothpick inserted into the center comes out clean.
Glaze
While the cake is baking, prepare the glaze: Gradually mix the remaining lemon juice into the powdered sugar. Use the lemon juice sparingly to achieve a thick consistency. You may not need all the juice.
Finish
Once the cake is done, remove it from the oven. While it's still warm, prick the entire surface with a fork.
Quickly spread the glaze over the warm cake, allowing it to seep into the holes.
Let the cake cool completely before serving.
Notes
The size of the slices is up to your own preference. I will often cut this cake into smaller slices which results in about 48 slices instead of 24. This is often beneficial if the cake is intended for a dessert buffet. Recipe SuccessIf the glaze is too thin, simply increase the amount of powdered sugar.