St. Louis Gooey Butter Cake

INGREDIENTS

• :
• 3 tablespoons milk, at room temperature
• 2 tablespoons warm water (about 110 degrees F)
• 1¾ teaspoons active dry yeast
• 6 tablespoons unsalted butter, at room temperature
• 3 tablespoons granulated sugar
• 1 teaspoon kosher salt
• 1 egg
• 1¾ cups all-purpose flour
• 3 tablespoons + 1 teaspoon light corn syrup
• 2 tablespoons water
• 2½ teaspoons vanilla extract
• ¾ cup (12 tablespoons) unsalted butter, at room temperature
• 1½ cups granulated sugar
• ½ teaspoon kosher salt
• 1 cup + 3 tablespoons all-purpose flour
• Powdered sugar, for sprinkling