For the veggie burgers: Soak the chickpeas in water overnight, then drain well. Place into a large pot and cover with fresh cold water. Add 6 cloves garlic, the whole celery stalks, carrot and onion. Bring to a boil and stir every 5 minutes until soft. Drain and let cool to room temperature. Discard the celery, carrot and onion, but keep the garlic.
Blend the remaining garlic, chopped celery, carrots, onions, parsley and cooked chickpeas in a food processor, in batches, making sure NOT to blend until completely smooth. Add the flour, olive oil, salt, basil, chili flakes, cumin, garlic powder, onion powder, oregano and eggs and mix well. Form into 1/3-pound patties or roll into balls.
For the sauce: Whisk together the hot sauce, mayonnaise, ketchup and relish.
For cooking the burgers: Place a nonstick saute pan over medium heat and dust the burgers with a coating of flour. Spray the pan with canola oil spray and cook the burgers for 3 minutes per side. Place 1 slice of the cheese on each burger, cover the pan and cook until the cheese has begun to melt, 30 seconds longer.
Top each bread thin with a heaping spoonful of the sauce and build the burgers with veggie burger patties, tomato, lettuce and onions.
Cook's Note: The veggie burgers are best when the mixture is made 1 day ahead.