01 - In a small mixing bowl, combine the finely ground coffee, brown sugar, smoked paprika, ground cumin, garlic powder, onion powder, sea salt, black pepper, and cayenne pepper. Stir until all spices are evenly incorporated.
02 - Divide the ground beef into 4 equal portions, each about 6 ounces. Gently shape into patties, pressing a slight dimple in the center to prevent puffing. Season both sides with kosher salt and freshly ground black pepper.
03 - Generously coat both sides of each patty with the prepared coffee rub, pressing gently to adhere. Set the patties aside at room temperature while preparing the sauce.
04 - In a saucepan over medium heat, combine the ketchup, apple cider vinegar, brown sugar, Worcestershire sauce, smoked paprika, garlic powder, onion powder, black pepper, salt, and liquid smoke if using. Stir well and simmer for 8 to 10 minutes, stirring occasionally, until the sauce has slightly thickened. Remove from heat and set aside.
05 - Preheat a grill or grill pan to medium-high heat. Lightly oil the grates to prevent sticking.
06 - Place the seasoned patties on the hot grill and cook for 4 to 5 minutes per side, or until the desired doneness is reached. During the last minute of cooking, top each patty with a slice of sharp cheddar cheese if desired, and close the grill lid to allow the cheese to melt.
07 - Place the brioche or hamburger buns cut-side down on the grill and toast for 1 to 2 minutes until golden brown.
08 - Layer lettuce, sliced tomato, and red onion on the bottom buns. Place the grilled coffee-rubbed patties on top, drizzle generously with the smoky BBQ sauce, and add dill pickle slices. Cap with the toasted bun tops and serve immediately.