Prep all ingredients per the instructions above.
In a mixing bowl, combine the ground beef, salt, black pepper, smoked paprika, Carolina-style tangy BBQ sauce, and Worcestershire sauce. Mix gently until just combined.
Shape the beef mixture into burger patties.
Heat a pan or grill over medium-high heat. Cook the burger patties, flipping once, until cooked through to your preferred doneness.
During the final minute of cooking, place a slice of cheddar cheese on each patty and cover to allow the cheese to melt.
Toast the hamburger buns on the grill or in a pan until lightly golden.
Assemble the burgers by placing arugula, tomato slices, pickle slices, and the cheeseburger patty on the bottom bun. Top with the remaining bun half.
Pour sparkling water over lemon slices and gently stir. Serve over ice if desired.
Serve the burgers with carrots, hummus, and the lemon sparkling water.