The day before braising, rub the flats liberally with the BBQ rub and place into a cooler uncovered to allow the meat to dry slightly and the spices to begin to penetrate the meat.
Remove from the cooler and allow to come to room temperature.
In a large rondeau or tilt skillet, heat a small amount of vegetable oil and brown the meat until golden brown on all sides. Do not crown the pan and do multiple batches if necessary.
Remove the meat from the braising pan and add the shallots, garlic, tomato paste thyme and bay leaves. Allow to cook until the shallots and garlic become soft.
Add the flats back to the pan and the veal stock and coca cola to just come to the top of the meat. Wrap in foil (or close lid) and allow to simmer for 4-6 hours, until fork tender. If doing in the oven, keep the temperature at 225 degrees.
Remove from heat and allow to cool in the braising liquid overnight.
Remove the flats from the cool liquid, removing all the fat. Bring to a simmer and then puree everything together. Run through a fine mesh strainer. Reserve the braising liquid for service.
At service time, heat the sauce and mount in a small amount of butter and adjust seasoning as necessary with grey salt and black pepper.
White Cheddar Grits: Bring the milk and ½ the butter to a boil. Add the grits and stir constantly for the first 5 minutes. Allow to simmer for 35-45 minutes or until tender. Stir in the remaining butter and the cheese. Adjust consistency, if necessary, using whole milk or heavy cream.
BBQ Rub: Combine all ingredients and reserve.
Pickled Vidalia Onions: Combine all ingredients except onions and bring to a boil. Pour over onions and refrigerate overnight.
Fried Quail Egg: In a cast iron skillet, heat a small amount of duck fat. Crack a quail egg into the pan and season with salt a pepper. Cook until white is set and yolk is still soft.