Special equipment: a Belgian-waffle iron; a deep pot or deep fryer
For the wings: Whisk together the buttermilk, salt, chili powder, black pepper, thyme and cayenne in a large bowl. Add the wings and refrigerate for 6 hours.
For the ham hock gravy: Combine the ham hocks and 2 quarts water in a large pot, bring to a simmer and cook for 3 hours. Add the celery, carrot and onion and simmer for 1 more hour.
Strain the stock and keep the ham hocks. Pick the meat off the ham hocks and reserve for the gravy.
Return the stock to the pot, bring to a boil and cook until reduced to 1 quart, about 30 minutes.
Melt the butter in a saucepan over medium heat. Whisk in the flour to make a roux. Cook the roux, stirring, until it gets a nice nutty brown color, about 5 minutes.
Slowly whisk the reduced stock into the roux to avoid lumps. Bring to a simmer, reduce the heat and simmer, stirring regularly, for 5 minutes. Add the ham hock meat and heavy cream, season with salt and pepper and continue to simmer for 15 minutes more.
For the waffle batter: Whisk together the flour, sugar, baking powder and salt in a large bowl.
In a separate bowl, whisk together the milk, eggs and melted butter.
Add the wet ingredients to the dry ingredients and whisk to combine. Some lumps in the batter are acceptable but not too many.
Preheat a Belgian-waffle iron and spray with nonstick cooking spray. Spoon 1/4 to 1/2 cup of the batter into the center of the waffle iron (depending on the size of the waffle iron) and close. Cook until the waffle is golden brown, 3 to 6 minutes, depending on the iron. Repeat with the remaining batter.
For the wing breading: Preheat the oil to 325 degrees F in a deep pot or deep fryer. Preheat the oven to 200 degrees F. Combine the flour, salt and pepper in a shallow bowl or plate.
Working with 3 to 4 wings at a time, dredge the wings in the flour and fry until the thickest part of the wing reaches an internal temperature of 165 degrees F, about 10 minutes. As the wings are cooked, transfer them to a rimmed baking sheet and keep warm in the oven.
To plate: Place a hot waffle on each of 6 plates. Stack 3 wings on top of each. Divide the gravy among the plates and garnish with the chopped scallions.