Begin by making the Pimento Cheese: Stir all the ingredients together in a bowl, and chill until serving.
Next, prepare the Buttermilk Onion Rings: In a Dutch oven, heat an inch of vegetable oil to 375 degrees. While the oil heats, mix the flour and spices together and divide the mixture between two bowls. Put the buttermilk in a third bowl. Dip the rings in first one bowl of flour, then the buttermilk, and then into the second bowl of flour. Fry the onion rings, about six at a time, until they're golden brown. Drain the cooked rings on wire rack over a pan, and sprinkle with salt.
Finally, make the burgers: Sprinkle the beef with the salt and pepper and form it into four patties. Heat a cast iron skillet on high heat. Drizzle the skillet with the oil and cook the burgers until your desired doneness. When the burgers are almost done, top each one with some of the pimento cheese.
Serve the burgers on the buns with the lettuce, tomato, and onion rings.