Slice the tops off the tomatoes (reserve for later) and gently core out the insides, leaving a thick wall on the tomatoes. Invert upside-down on paper towel to drain. Set aside.
Combine the tuna with the flavored tuna oil, cooked rice, red onion, celery, parmesan, salt, and parsley.
Stuff the tomatoes with the tuna mixture and place in a baking dish or baking sheet pan. Place the reserved tomato tops on the baking sheet pan off to the side of the stuffed tomatoes. Lightly oil the tomatoes and tops.
Bake for 10-15 minutes or until the tomatoes are tender and the tuna filling is heated through.
While the tomatoes bake, make the dressing. Whisk together all the balsamic dressing ingredients (olive oil, balsamic vinegar, lemon juice, mustard, garlic, salt, and pepper).
After the tomatoes are baked, drizzle the dressing over the tomatoes. Finish with the roasted tomato tops. Serve warm or at room temperature.