In a large bowl, whisk together all brine ingredients. Put the chicken breasts into the buttermilk brine and allow to soak for 30 minutes, or up to 24 hours.
In a separate large bowl, whisk together flour, cornstarch, baking powder, pepper, granulated garlic and onion, paprika, cayenne, and oregano. Take two or three tablespoons of the buttermilk brine into the flour and toss the brine and flour together with a fork or whisk to create some chunky clumps of flour. This will help create better crag on your fried chicken.
Dredge your chicken breasts through the seasoned flour mix, covering each side well in the flour. Set on a clean plate until all chicken is coated in flour. To make the crust extra crispy and crunchy, re-dredge by dipping back in buttermilk brine, shaking off the excess, and coating the chicken in flour once again, and allowing to rest on a plate, repeating until all the chicken is re-dredged. Let the chicken rest on the plate for ten minutes as your oil is heating up to temperature.
In a large heavy bottom pot or Dutch oven, heat 5-6 cups of vegetable oil to 325 degrees F. Have a wire rack sitting on a paper towel-lined baking sheet prepped and ready for the chicken.
Once oil is to temperature, add two chicken breasts to the oil and allow to fry for 4-5 minutes, until golden brown and cooked through. Place on the wire rack to drain the excess oil and cool.
To melt cheese onto the chicken, top chicken with sliced cheese and place on a baking sheet. Put into the oven on low broil to melt the cheese. Keep an eye on it, melting won't take more than a minute or two.
Assemble sandwiches with preferred toppings and garlic aioli smeared on both buns, top and bottom. Serve hot.