Tear arugula into small pieces. (set aside). Cut tomatoes into 1/2 inch cubes (set aside). Cut hearts of palm into 1/2 inch rounds (cut crosswise) (set aside). Cut avocados into 1/4 wedges, drizzle with the juice of one lemon (set aside).
On a large serving platter arrange the arugula, top with tomatoes, followed by a layer of hearts of palm. Top the salad with avocado wedges and drizzle with oil. Salt and pepper to taste.
Slice Parmigiana with a sharp pairing knife into paper-thin shavings. Distribute cheese and pine nuts on top of salad.