In the food process, process the goat cheese until smooth. Add lemon zest and juice and blend until incorporated. Slowly add whipped cream tablespoon by tablespoon until you reach the desired consistency. Salt and pepper to taste.
Whisk all dressing ingredients together in a small bowl. Set aside.
Arrange the goat cheese on a plate or shallow tray. Top with peaches, tomatoes, pistachios, and watercress. Drizzle dressing on top. Serve immediately.