Combine first 6 ingredients in a food processor; process until smooth. With processor on, slowly pour oil through food chute; process until well blended. Pour tofu mixture into a small bowl; stir in parsley.
Combine romaine lettuce and tofu mixture in a large bowl, and toss to combine. Arrange 1 1/2 cups salad on each of 8 plates, and top each serving with about 1 teaspoon Parmesan cheese.