For dressing, whisk balsamic vinegar with mustard. Slowly pour in olive oil while whisking. Season to taste.
If dressing seems thick, whisk in a tablespoon or 2 of water (this allows the dressing to coat the arugula without weighing them down).
To assemble the salad, arrange arugula on a platter. Remove core from pineapple and slice as thinly as possible (on a mandolin is best). Arrange pineapple over arugula.
Slice red onion and arrange on salad. Sprinkle pine nuts over. With a vegetable peeler or cheese knife, pull curls or thin shards of Piavé over.
Drizzle dressing over, season lightly and serve.