Special equipment: a deep-frying thermometer
For the clams and peppers: Put the clam bellies and peppers in a bowl, add the buttermilk and let soak, refrigerated, for at least 8 hours or overnight.
For the sauce: Combine the mayonnaise, pickles, lemon juice, capers and parsley in a bowl. Season with salt and pepper.
For the sandwiches: In a bowl, toss the shredded lettuce with the vinegar and set aside.
Heat the oil in a large, deep, straight-sided pot until a deep-frying thermometer registers 360 degrees F. Line a plate with paper towels.
Combine the cornmeal, flour, Parmesan, garlic powder and paprika in a shallow dish. Season with salt and pepper.
Using a slotted spoon, scoop the clam bellies and peppers out of the buttermilk, leaving the excess behind. Toss in the flour-cheese mixture to evenly coat.
Fry the clams and peppers in the hot oil until golden brown, about 2 minutes. Drain on the towel-lined plate and season immediately with salt and pepper.
Heat a griddle or skillet over medium heat. Slice the buns in half lengthwise and butter the cut sides. Cook the buns butter-side down until toasted.
Spread the sauce on both sides of the buns and top with lettuce, fried clam bellies and peppers.