Using a fryer or a large pot, heat oil to 350 degrees F.
Cut the chicken wings at the joint to yield a wingette and drumette from each wing. Sprinkle the wings with salt. Deep-fry the wings until golden and crispy, 12 to 15 minutes.
Meanwhile, in a medium saucepan over medium-low heat, melt the butter. Add the pepper jelly and continually whisk until it lightly bubbles, 5 to 10 minutes. Turn the heat down to low and allow to simmer as the wings continue to cook. When the wings are ready, add directly to the pan and toss.
Serve immediately with blue cheese and carrots or celery.