Divide beef into 4 equal portions. Roll each portion into a ball; make a pocket in the side of each ball, and insert 1 tablespoon blue cheese. Roll back into a ball, and flatten into a 3 1/2- inch pattie. Cover and chill.
Heat oil in a large nonstick skillet over medium- high heat. Add onion, and sauté 12 to 14 minutes or until golden. Add mushrooms; sauté until tender and liquid is absorbed. Add salt and pepper. Set aside, and keep warm.
Place patties on grill rack coated with cooking spray; grill, covered, 6 minutes on each side or until done.
Place pattie on bottom half of roll; top each with 1/4 cup onion mixture. Spread 1 teaspoon mustard on cut side of remaining roll halves. Cover burgers with roll tops.