Add tomato, parsley, olives, vinegar, mustard, oil, salt, pepper, and garlic to a large bowl; combine well. Finely chop 1 heart of palm and mix into the tomato mixture. Wrap with plastic wrap and place in refrigerator for at least 2 hours.
Slice 2 hearts of palm in half lengthwise. Lay 2 hearts of palm halves, 3/4 cup lettuce, and 3/4 cup tomato mixture on each of 2 serving plates. Sprinkle 1/2 teaspoon cheese on top of each salad.