Fill a deep, heavy pot halfway with vegetable oil (or use a deep fryer) and heat the oil to 360 degrees F.
Put the Buffalo sauce, sweet chili sauce, honey and butter in a saucepan and bring to a simmer; simmer for 10 minutes. Toss the chicken in the sauce, season with salt and pepper and set aside to cool slightly, about 10 minutes.
Whisk together the egg and 1 tablespoon water in a small bowl for the egg wash and set aside.
Take a wonton wrapper (cover the rest with a damp towel) and put a small amount of the chicken mixture--about 2 level tablespoons--in the middle of it. Add a few pieces of blue cheese crumbles, being careful not to go too far outside of the middle of the wonton--we don't want the cheese to ooze out when frying. Next, brush all 4 corners with the egg wash, then seal the corners by pinching each opposite corner together to make that famous wonton shape; make sure there are no holes for the filling to leak out. Repeat with the remaining ingredients.
Now in the fryer they go! Fry the wontons in batches until golden brown, 3 to 4 minutes total. Drain briefly on a rack or paper towel-lined plate. Serve hot with carrot sticks, celery sticks and ranch dressing.