Special equipment: a deep-fry thermometer, a melon baller and 1 1/2-inch, 2-inch and 2 1/2-inch round biscuit or cookie cutters
Fill a large, heavy-bottomed pot halfway with oil, attach a deep-fry thermometer to the side of the pot and heat to 350 degrees F. Line a baking sheet with paper towels and set aside.
Whisk together the cider, flour and 1 teaspoon cinnamon in a large bowl until no lumps remain and the batter is completely smooth. Stir together the sugar and remaining 1/2 teaspoon cinnamon in a small bowl.
Slice the apples in half crosswise (not through the stem). Scoop out the core and seeds using a melon baller, being careful not to go all the way through the apple. Have ready a 1 1/2-inch, 2-inch and 2 1/2-inch round biscuit or cookie cutters. Make 3 concentric circles on each apple half starting with the smallest biscuit cutter around the core and then working out with a slightly bigger cutter each time. Press each ring down into the apple but don't go through the skin (you should have 3 rings). This keeps the apple intact. (See Cook's Note.) Flip an apple over and, visualizing a quarter placed on top of the stem in the center, cut slits through the apple about 1/2 inch apart, circling around the quarter. This also keeps the apple intact. Repeat with the remaining apples.
Use your hands to gently pull apart the outer layers of the apple while keeping the skin intact. This will allow the batter to sink into the cuts and help the apple bloom.
Sprinkle each apple half with 1 teaspoon of the cinnamon-sugar mixture and let sit for 5 minutes. Stuff the centers with 4 marshmallows each. Place 2 apples at a time in the batter, using a slotted spoon to turn them and evenly coat. Lower each apple cut-side down into the hot oil with the slotted spoon and fry until crispy and golden brown on the bottom, about 3 minutes. Flip the apples over and continue to fry until the apples are tender and golden brown and crispy on the top, 2 to 3 minutes more. Transfer with a slotted spoon to the prepared baking sheet to drain. Repeat with the remaining apples, being sure to bring the oil temperature back to 350 degrees F before frying again.
Meanwhile, stir the caramel sauce and salt in a small bowl until well combined. Dollop each apple with whipped cream and drizzle with the caramel sauce. Serve with the remaining sauce for dipping.
If you do not have biscuit cutters you can use a sharp paring knife to cut the circles into the apple halves.
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