Preheat the oven to 425 degrees. Remove the top quart of tomatoes, and scoop out the core and seeds. Season the tomato cups with salt and pepper.
Chop ¼ cup of the tomato core. Discard the remaining seeds and cores.
In a bowl, slightly mash about half the beans, then stir in chopped tomato, ½ cup breadcrumbs, ¼ cup Parmigiano-Reggiano, garlic, mustard, lemon zest, and lemon juice. Gently fold in tune and remaining beans. Season with salt and pepper.
Transfer tomato shells to a baking dish, and fill each with the tuna mixture, dividing evenly and mounding slightly.
In a bowl, stir together the remaining ½ cup breadcrumbs, ¼ cup of Parmigiano-Reggiano, and oil. Season with salt and pepper.
Top the tomato shells with the breadcrumb mixture. Loosely cover with foil and bake until softened lightly, about 30 minutes. Uncover and bake until the breadcrumbs are golden brown, about 5 minutes. Serve immediately.