Gooey Butter Cake

Ingredients

• 3 tablespoons milk, at room temperature
• 1 ¾ teaspoons active dry yeast
• 6 tablespoons unsalted butter, at room temperature
• 3 tablespoons sugar
• 1 teaspoon kosher salt
• 1 large egg
• 1 ¾ cups all‑purpose flour
• 12 tablespoons (1 ½ sticks) unsalted butter, at room temperature
• ¼ cup heavy cream, at room temperature
• 3 tablespoons light corn syrup
• 1 tablespoon vanilla extract
• 1 cup granulated sugar
• ¼ cup packed light brown sugar
• ½ teaspoon kosher salt
• 1 cup plus 3 tablespoons all‑purpose flour
• Powdered sugar, for topping