Heat oil in a medium nonstick skillet over medium-high heat. Add chicken to pan; sprinkle with 1/8 teaspoon salt and black pepper. Sauté 5 minutes or until chicken is done. Remove chicken from pan. Add red bell pepper and next 5 ingredients (red bell pepper through garlic) to pan; sauté 6 minutes or until tender. Stir in chicken and pepper sauce; remove from heat.
Slice each roll in half horizontally, cutting to, but not through, other side. Place 1 cheese slice and 1 cup chicken mixture on bottom half of each roll, and gently press roll halves together.
Heat a large nonstick skillet over medium heat; add 2 sandwiches. Place a cast-iron or heavy skillet on top of sandwiches; press gently to flatten. Cook 4 minutes on each side or until cheese melts and bread is toasted (leave skillet on sandwiches while they cook). Repeat with remaining sandwiches.