Heat grill to medium-high heat.
To prepare the hot sauce: combine Tabasco, butter, cayenne, and a pinch of salt and pepper in a small bowl. Generously brush both sides of burger patties with mixture, and set aside.
To prepare the blue cheese sauce: combine blue cheese, sour cream, mayonnaise, buttermilk, 1 teaspoon vinegar, and a generous grind of black pepper in another small bowl. Whisk until smooth.
To prepare the slaw: toss celery with onion, parsley, oil, mustard, 2 teaspoons vinegar and a pinch of salt and pepper in a medium bowl.
Season patties with salt and pepper, and place over direct heat on the grill. Brush with Tabasco mixture. Cook 2-3 minutes, basting once, and flip. Cook another 2 minutes, until medium rare. Place buns cut-side-down on grill, and cook until toasted.
Place burgers on buns, top with celery slaw, and drizzle with blue cheese mixture.