Preheat the oven to 400 degrees F. Combine the hot sauce, butter and garlic in a small saucepan and bring to a simmer over medium-low heat. Cook until slightly thick, about 15 minutes. Discard the garlic.
Remove the meat from the chicken, discard the skin and shred the meat into small pieces (you should have about 2 cups). Toss in a bowl with 1/2 cup of the sauce. Whisk 1/3 cup of the heavy cream and the blue cheese in another bowl to combine.
Spread the tortilla chips in an even layer on a large pizza pan or ovenproof skillet lined with parchment paper. Scatter the chicken on top, and then spoon 1/4 cup more sauce over the meat and chips. Sprinkle the sliced celery and Cheddar evenly over everything. Dollop half of the blue cheese sauce over top, reserving the rest for additional topping. Bake until hot and the cheeses melt, about 10 minutes.
Top with the celery leaves. Stir the remaining 1 tablespoon heavy cream into the reserved blue cheese sauce and drizzle over the finished nachos.