Heat a medium nonstick skillet over medium-high heat.
Add onion to pan; coat onion with cooking spray. Cook 15 minutes, stirring frequently, until tender and browned.
Remove pan from heat. Finely chop 1/4 cup onion, and place in a medium bowl, reserving remaining onion in pan.
Add salt, pepper, and beef to caramelized onion in bowl; mix well. Divide beef mixture into 8 equal portions, shaping each into a 1/4-inch thick patty.
Heat a grill pan over medium-high heat.
Place patties on grill pan. Grill 3 minutes on each side, until a thermometer registers 160 or until desired degree of doneness.
Place mayonnaise and blue cheese in a food processor; process until smooth.
Spread blue cheese mixture evenly on bottom halves of buns.
Place 1 patty on bottom half of each bun. Top patties evenly with arugula, tomato slices, and remaining caramelized onion; cover with bun tops.