Cook vegetables: Heat the oil over low heat. Add chickpeas, beets, and radish. Cook and stir for 3 minutes. Add the zucchini blossoms. Cook and stir for 2 more minutes.Season with salt and pepper to taste. Remove from the heat and cool to room temperature.
Assemble: Arrange the arugula on a plate. Top with the cooked ingredients, then tomatoes.Drizzle with the balsamic vinegar. Top with the shaved parmesan.