Lemon Yogurt Cake

INGREDIENTS

• 3 extra-large eggs
• 2 tablespoons freshly squeezed lemon juice
• 1/3 cup freshly squeezed lemon juice
• 1/2 teaspoon pure vanilla extract
• 1 1/2 cups all-purpose flour
• 2 teaspoons baking powder
• 1/2 teaspoon kosher salt
• 1/2 cup vegetable oil
• 1 cup confectioners' sugar
• 2 teaspoons grated lemon zest (2 lemons)
• 1 1/3 cups sugar, divided
• 1 cup plain whole-milk yogurt