Preheat oven to 350 degrees F. Spray a 9-inch cake pan with nonstick cooking spray and set aside.
In a large bowl, stir sugar and lemon zest together to create a damp mixture that resembles damp sand. Stir in the eggs and vanilla until smooth.
In a liquid measuring cup, stir milk, vinegar, and lemon juice together. Set aside.
In a separate bowl, whisk flour, baking soda, baking powder, and salt together to combine.
Alternate stirring in wet and dry ingredients until everything is added into the cake batter. Gently stir in the poppy seeds and melted butter.
Pour into prepared pan and bake 45-55 minutes or until baked thoroughly and a toothpick comes out clean after being inserted. Cool 15 minutes in the cake pan before removing to a rack to cool completely.
For the frosting, whip all ingredients together until light and fluffy. Spread over cooled cake and serve.
Notes
*or use 1/2 cup buttermilk instead of milk and white vinegar mixture