Prepare a charcoal or gas grill and heat to medium high (approximately 400 degrees).
Place all of the blue cheese spread ingredients into the bowl of a mini food processor and process for 5 Đ 10 seconds or until mixture is well incorporated and smooth. Set aside and keep cool until ready to use.
In a small bowl, combine all of the whole grain mayo ingredients and stir well. Cover and keep cool until ready to use.
Place all of the patty ingredients into a large bowl, being careful not to overwork the meat, mix well to incorporate all the ingredients. Divide into 6 equal portions, form each portion into a ball, then flatten until they are the size of the bun.
Oil the grill grate with a paper towel that has been folded and coated with the cooking oil and pinched between tongs.
Place the patties onto the grill and cook for approximately 4 minutes, flip, then top each patty with a tablespoon of the cherry jam or preserves. Cook an additional 4 minutes or until the internal temperature reaches approximately 130 degrees for medium rare to medium.
Remove the patties from the grill, place on a plate and tent with foil to keep warm until ready to use.
Butter the inside of the buns with the softened butter. Place the buns on the hot grill, buttered sides down. Toast the buns for approximately 30 seconds to 1 minute or until they are warm and lightly toasted with light grill marks.
Spread bun bottoms with the blue cheese spread and top halves with mayo. Top bottoms of the buns with a hamburger patty, arugula, and the top half of the bun.