1. 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.
2. 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.
3. 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.
4. 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.