Preheat oven to 350 degrees
In a stand mixer with the paddle attachment, cream together the butter and sugar until light and fluffy
In a medium bowl, whisk together flour, salt and baking powder
Add eggs, vanilla and lemon zest and beat well
Add in the flour and milk, alternating between and ending with the flour
Mix the cake batter until well combined
Fold in blueberries
Pour the batter into a greased or parchment paper lined square 8" inch pan
Bake at 350 for 30 minutes or until the top is golden brown and a toothpick comes out clean from the center
Let cool on a wire rack for 30 minutes before frosting
FROSTING
In the stand of a mixer, beat the butter until light and creamy (about 2-3 minutes)
Gradually add the powdered sugar, one cup at a time, beating slowly until the sugar is fully incorporated. After each addition, increase the speed to medium and beat until the mixture is smooth and creamy. Scrape down the sides of the bowl as needed.
Add the vanilla extract and 1-2 tablespoons of milk the mixture. Beat on medium speed for about 1 minute. If the frosting is too thick, add more milk or cream, one tablespoon at a time, until you reach the desired consistency.