Heat olive oil in a large nonstick skillet over medium heat.
Add mushrooms and onion; cover and cook 7 minutes or until onion is tender, stirring occasionally.
Remove from heat; cool.
Combine the mayonnaise, basil, and black pepper.
Spread 1 tablespoon mayonnaise mixture on each bread slice; layer each of 2 slices with 1/3 cup bell peppers, 1/2 cup mushroom mixture, and 1 slice of cheese. Top with remaining bread slices.