In a small bowl, whisk together mustard and oil until thick; spread on bread. Layer bottom half of bread with some of the lettuce, then cheese, tomatoes, and parsley. Season with salt and pepper. Top with remaining lettuce and bread.
Wrap sandwich tightly in plastic; place on a baking sheet. Top with another sheet, and weight down with canned goods or a heavy skillet. Refrigerate at least 1 hour and up to overnight to meld flavors. Cut in half, and serve.