Recommended Equipment: A shallow baking dish with two-or three-quart capacity.
Arrange a rack in the top half of the oven and preheat to 375ºF. Fill a large pot with water (at least five quarts) and bring it to a boil.
Dump them all into the boiling water, cover the pot until the water boils again, then cook uncovered, for 10 minutes or so, until they are just cooked through –- tender but still firm enough to snap.
Drain the beans briefly in a colander, then put them in a big kitchen bowl. Sprinkle 1/4 teaspoon of salt on the hot beans and toss them so they're all seasoned. Let the salt melt and the beans cool for a couple of minutes.
Meanwhile, rinse and dry the tomatoes. If they're larger than an inch, slice them in halves, otherwise, leave them whole. Cut the mozzarella into 1/2—inch cubes. Slice the basil leaves into thin shreds or a chiffonade.
Toss the grated cheese and bread crumbs together in a small bowl. Lightly grease the insides of the baking dish with a teaspoon or more of the butter. Sprinkle 1/4 cup of the cheese-and—bread-crumb mix all over the bottom of the dish.
When the beans are no longer steaming, drop the tomatoes, cubes of mozzarella and basil shreds on top. Drizzle the olive oil over all, sprinkle on the remaining 1/4 teaspoon salt and toss together a few times. Sprinkle 3/4 cup of the cheesy bread crumbs on top and toss well, so everything is coated.
Turn the vegetables, scraping up all the crumbs, into the baking dish and spread them in an even layer. Sprinkle over the remaining 1/4 cup of crumbs, cut the rest of the butter in small pieces and scatter them all over the top. Place the dish in the oven.
Bake the gratinate for 10 minutes, then rotate it back to front and bake another 10 minutes. Check to see that it is browning and bake a few minutes more, until the gratinate is dark golden and crusted. (If the crumbs still look pale after 20 minutes in your oven, raise the temperature to 400 degrees or 425 degrees and bake until done.)
Serve the hot gratinate in the baking dish. Recipe serves 6.