To make the vinaigrette – Place all the ingredients in the bowl of a food processor. Process until creamy, about 1 minute, scraping the sides of the bowl once. Transfer to a small bowl.
Divide the arugula into 4 salad bowls. Top with the avocado and tomato pieces. Drizzle with the vinaigrette. Garnish with the crispy wontons. Sprinkle with the pepper and serve immediately.