1. Combine 2 teaspoons olive oil, rosemary, and chicken in a large zip-top plastic bag. Seal and marinate in refrigerator 30 minutes.
2. Heat a large nonstick skillet over medium-high heat. Add remaining 4 teaspoons oil to pan. Add sun-dried tomato, red pepper, and garlic; sauté 1 minute or until garlic begins to brown. Add spinach; cook 1 minute or until spinach barely wilts. Stir in 1/8 teaspoon salt; set aside.
3. Heat a grill pan over medium-high heat; coat with cooking spray. Sprinkle chicken with remaining 1/4 teaspoon salt and black pepper. Cook chicken 3 minutes on each side or until done. Remove chicken from pan; keep pan on medium-high heat.
4. Top each of 4 bread slices with 1 tablespoon cheese, 1 chicken cutlet, one quarter of spinach mixture, 1 additional tablespoon cheese, and remaining 4 bread slices.
5. Recoat grill pan with cooking spray. Arrange 2 sandwiches in pan. Place a cast-iron or heavy skillet on top of sandwiches; press gently to flatten. Cook 4 minutes on each side (leave skillet on sandwiches while they cook). Repeat procedure with remaining 2 sandwiches. Cut each sandwich in half; serve immediately.