In a medium bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and kosher salt. Add the eggs and milk and whisk until smooth. Set aside.

Sprinkle about ¼ cup of the shredded Gruyère cheese over 1 slice of white sandwich bread. Top with 2 slices of deli ham and 2 slices of deli turkey, then sprinkle another ¼ cup of shredded Gruyère cheese over the meat. Place a second slice of white sandwich bread on top.

Pour 3 inches of vegetable oil into a deep saucepan or Dutch oven. Have ready a wire rack lined with paper towels to use for draining. Heat the oil to 350°F on a deep-fry thermometer.

Working with 1 sandwich at a time, carefully dip it in the batter, letting the excess batter drip back into the bowl. Slowly lower a battered sandwich into the oil and fry until golden brown on the bottom, about 4 minutes. Using a spatula, flip the sandwich over and fry until golden brown on the other side, about 4 minutes. Remove the sandwich to the paper towel-lined rack to absorb the excess grease. Repeat to fry the remaining sandwiches.

Using a sifter or fine-mesh sieve, gently tap 2 teaspoons of powdered sugar over each sandwich.

In a small, microwave-safe bowl, stir together the seedless raspberry preserves and 2 teaspoons of water. Microwave on high for 30 seconds, until loosened.

Serve each sandwich with about 2 tablespoons of raspberry preserves for dipping.