In a medium bowl, combine tuna, pesto, red peppers, mayonnaise, and Parmesan. Mix well and season to taste with salt and black pepper. Spoon tuna mixture onto bread slices and place on a foil-lined baking sheet. Top the tuna with cheese. Broil 2 minutes, until cheese melts.
For the salad:
In a small bowl, whisk together oil, vinegar and mustard and season to taste with salt and black pepper. Arrange lettuce on a serving plate and top with grapefruit segments and walnuts. Pour dressing over salad and serve.