1/2 pound unsalted butter, at room temperature
2 1/2 cups granulated sugar
4 extra-large eggs, at room temperature
1/3 cup grated lemon zest, (6 to 8 large lemons)
3 cups all-purpose flour
1/2 teaspoon baking powder
1/2 teaspoon baking soda
1 teaspoon kosher salt
3/4 cup freshly squeezed lemon juice
3/4 cup buttermilk, at room temperature
1 teaspoon pure vanilla extract
2 cups confectioners’ sugar
3 1/2 tablespoons freshly squeezed lemon juice