1/4 cup whole milk 2 teaspoons active dry yeast 6 tablespo plus more for pan ) 3 tablespoons granulated sugar 3/4 teaspoon salt 1 egg 1 3/4 cups all-purpose flour 3/4 cup (1 1/2 sticks) butter ( softened ) 1 1/2 cups granulated sugar 1/2 teaspoon salt 1/4 cup light corn syrup 1 1/2 teaspoons vanilla extract 2 eggs