Heat closed contact grill or panini maker 5 minutes.
Meanwhile, on cutting board, carefully unroll dough. Cut into 8 rectangles. Place 2 rectangles on grill; close grill. Cook 1 to 2 minutes or until lightly browned. Remove from grill. Repeat with remaining rectangles.
In 8-inch nonstick skillet, heat oil over medium heat until hot. Add bell pepper and onion; cook 3 to 5 minutes, stirring frequently, until vegetables are tender.
Top each of 4 rectangles with one-fourth of the beef, one-fourth of the pepper mixture and 1 slice cheese. Top with remaining rectangles.
Place 2 sandwiches on grill; close grill. Cook 2 to 3 minutes or until cheese is melted. Repeat with remaining sandwiches.