Combine first 7 ingredients in a small bowl. Rub spice mixture over one side of steak; let stand 10 minutes.
Place steak on grill rack coated with cooking spray; grill 8 minutes on each side or until desired degree of doneness. Let steak stand 10 minutes. Cut steak diagonally across grain into thin slices.
Cut bell peppers in half lengthwise; discard seeds and membranes. Flatten peppers with hand. Place peppers skin-side down on grill rack; grill 12 minutes or until blackened. Place peppers in a zip-top plastic bag; seal. Let stand 10 minutes. Peel and cut each half into quarters.
Combine mayonnaise, cheese, juice, and 1 garlic clove in a small bowl, stirring well. Spread about 1/4 cup mayonnaise mixture onto cut side of each bread half. Arrange beef evenly over bottom half; top with peppers. Cover with top bread half, pressing gently. Cut sandwich into 4 wedges.