Combine first 4 ingredients and divide meat into 4 equal amounts. When forming each patty, nestle a pile of blue cheese crumbles into the center of the meat, and gently form patty around cheese.
Brush or drizzle burgers with extra-virgin olive oil and grill on indoor electric grill preheated to high for 7 to 8 minutes on each side. On an outdoor grill, cook 6 minutes on each side 6 inches from hot coals or over medium high gas flame with the grill lid closed. For preparation with no additional oil, broil 4 inches from broiler 7 minutes on each side.
Serve burgers on split rolls with lettuce, tomato, and blue cheese dressing.