Apple Fritter Doughnuts

INGREDIENTS

• :
• 2¼ teaspoons (1 packet) active dry yeast
• ⅔ cup whole milk, warm to the touch
• 3¼ cups + 2 tablespoons all-purpose flour, divided
• 4 egg yolks
• ½ cup granulated sugar
• ⅓ cup apple cider
• ¼ cup unsalted butter, melted
• 1 tablespoon vanilla extract
• 1 teaspoon kosher salt
• ½ teaspoon ground cinnamon
• ¼ cup unsalted butter
• 1 vanilla bean
• 7 Granny Smith apples, peeled, cored and chopped
• ¼ cup granulated sugar
• 1 cup apple cider
• ¼ cup apple cider vinegar
• ½ cup + 2 tablespoons powdered sugar
• ¼ cup heavy cream
• ½ teaspoon vanilla extract
• ½ teaspoon kosher salt
• 2 quarts vegetable oil, for frying