St. Louis Gooey Butter Cake

Ingredients

• warm water (110 degrees)
  1/4 cup
• instant yeast
  4 1/2 teaspoons
• warm milk (110 degrees)
  1/2 cup
• granulated sugar
  1/3 cup
• pure vanilla extract
  2 teaspoons
• (1/2 stick) unsalted butter

  softened
  1/4 cup
• egg
  1 unit
• salt
  1/4 teaspoon
• all-purpose flour

  divided
  2 1/2 cups
• granulated sugar
  2 1/2 cups
• (2 sticks) unsalted butter

  softened
  1 cup
• salt
  1 Dash
• egg
  1 unit
• light corn syrup
  1/4 cup
• all-purpose flour
  2 1/3 cups
• warm water (110 degrees)
  1/4 cup
• pure vanilla extract
  2 teaspoons
• Confectioners' sugar

  for sprinkling
  1 unit