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, roughly 6 ounces each. Gently shape each portion into a patty about ¾ inch thick, pressing a slight dimple in the center to prevent puffing. Season both sides of each patty with kosher salt and freshly ground black pepper.
03 - Generously coat both sides of each patty with the prepared coffee rub, pressing the seasoning gently into the meat. Set the patties aside at room temperature while preparing the sauce to allow the flavors to penetrate.
04 - In a medium 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. Whisk to blend and bring to a gentle simmer. Cook for 8 to 10 minutes, stirring occasionally, until the sauce thickens slightly and coats the back of a spoon. Remove from heat and set aside.
05 - Preheat an outdoor grill or grill pan to medium-high heat, approximately 400°F. Lightly brush or oil the grates to prevent sticking.
06 - Place the coffee-rubbed patties onto the hot grill. Cook for 4 to 5 minutes per side for medium doneness, adjusting time for preferred temperature. During the final minute of grilling, lay a slice of sharp cheddar cheese on each patty and close the grill lid to allow the cheese to melt evenly.
07 - Place the brioche or hamburger buns cut-side down on the grill. Toast for 1 to 2 minutes until golden brown and lightly crisped at the edges.
08 - Layer lettuce leaves, tomato slices, and red onion rings on each bun bottom. Place the hot cheese-topped coffee rub patty on top, drizzle generously with the smoky BBQ sauce, and add dill pickle slices. Cap with the toasted bun top and serve immediately while hot.