Lemon Cake

INGREDIENTS

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