Cook the rice according to package directions; cool.
For the vinaigrette, combine Dijon mustard, balsamic vinegar, extra virgin olive oil, salt and pepper in a small dish. Taste the vinaigrette and adjust accordingly. Toss the cooled rice with the vinaigrette, but reserve a little for the end.
Add handfuls of tomatoes, olives, and mozzarella cheese into the rice. Add chopped fresh basil. Gently mix.
Drizzle with the remaining vinaigrette, and add salt and pepper. Serve cold or room temperature, or heated to warm. Garnish with more fresh basil leaves.