Philadelphia Butter Cake

Ingredients

• 1/4 cup (about 2 ounces) granulated sugar
• 1/4 cup (4 tablespoons) salted butter
• 1/4 teaspoon salt
• 1 large egg
• 1 (1/4 ounce) packet active dry yeast
• 1/2 cup warm milk (105-115°f)
• 2 1/4 cups (about 12 ounces) flour, sifted
• 2 teaspoons vanilla extract
• 1 cup (16 tablespoons) unsalted butter
• 2/3 cup (about 3 ounces) flour
• 2 cups (about 16 ounces) superfine sugar
• 2 large eggs
• 4 tablespoons milk
• 1 teaspoon clear vanilla extract