Special equipment: a deep fryer
Heat the oil in the deep fryer to 360 degrees F.
In a medium bowl combine the 2 1/2 cups flour, cornmeal, brown sugar, baking soda, and salt. Whisk together the buttermilk, water, eggs, and vanilla. Add the wet ingredients to the dry and mix to form a lumpy batter. Dredge the apple rings into the remaining flour, shaking off any excess. Dip the apples in batter and fry until golden, about 2 minutes per side. Remove from the oil and place on a paper towel to absorb the excess oil. Serve with Caramel Drizzle.
In a medium pot combine the water and sugar. Over high heat bring to a boil and cook until the syrup becomes amber, about 7 minutes. Remove from the heat and whisk in the apple juice slowly, being careful of the steam released. Add the cinnamon and star anise.
Return to high heat and bring to a boil. Reduce heat to medium and simmer until reduced to 1 cup of liquid, about 20 minutes. Discard the cinnamon stick and star anise and cool.
Store for up to 1 month in the refrigerator.