For the dressing: In a large bowl, whisk together the olive oil, vinegar, Dijon mustard and 1/2 teaspoon salt. Set aside.
For the salad: Heat the olive oil in a large skillet over medium heat. Add the onion and 1/4 teaspoon salt and cook, stirring often, until soft and golden brown, about 12 minutes. Add the onions to the dressing and stir to coat.
Bring a large pot of salted water to a boil. Cook the orzo until al dente, about 10 minutes. Drain it well and, while it is still warm, add to the bowl of dressed onions. Stir in the fennel and dried cranberries and allow to cool to room temperature, about 20 minutes. Add the arugula and mozzarella and toss to combine. Serve at room temperature or refrigerate until ready to serve.
Cook's Note: If serving the next day, a drizzle of olive oil will help to bring this salad back to life.
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