Program your grill to about medium heat and brush the grates until they are clean.
Place the ground beef, water, barbeque rub, grated garlic, grated garlic, and basil into a large bowl and stir just until combined.
Portion the burger meat into six evenly shaped patties and make an indent into each burger patty with your thumb.
Place the burger onto the grill and cook for 4 minutes, turn the bbq burger over and cook it for an additional 2 minutes.
Top the burgers withthe cheddar cheese and cook it for 2 minutes until the burger's internal temperature reaches 160ºF.
Spread a 1/2 tablespoon of butter onto the inner piece of each hamburger bun.
Grill your hamburger buns for 1-2 minutes until they are evenly toasted.
To make the bbq mayo whisk the mayonnaise, bbq sauce, lemon juice, smoked paprika, and cayenne pepper in a bowl.
Spread the bbq mayo onto the hamburger buns, add the bbq burger, top with your favorite toppings and place the top burger bun on top.
Serve and enjoy!