In a small mixing bowl, thoroughly combine the salt, garlic powder, paprika, brown sugar, black pepper and cayenne. Set aside.
Using a sharp knife, cut the tubular top portion away from the globe-shaped bottoms of both squash. Using the knife or a mandoline, shave the tops into chips. Submerge the chips in a deep container with ice water for 10 minutes (this removes any extra starch and makes the chips crispy). Strain the chips and pat dry.
Meanwhile, using an instant-read thermometer, bring 3 inches of duck fat to 325 degrees F in a heavy gauge Dutch oven over medium heat. Working in batches, fry the chips until they are golden and crispy, 5 to 7 minutes. Transfer with a fine mesh strainer to a paper-towel-lined dish. Season immediately with a sprinkle of spice mix. Repeat until all chips are fried. Transfer to a large bowl and serve.