Begin by preheating your griddle to 425 to 450 degrees.
Place ground chuck in a large mixing bowl, breaking-up loosely. Add salt, black and white pepper and lightly blend together.
In a separate bowl, blend together the shredded Mozzarella, grated Parmesan cheese, extra virgin olive oil and fresh chopped basil.
Dice tomatoes and place in a colander, in the sink, or over a bowl; sprinkle with salt and allow them to macerate for 10 to 15 minutes.
Once macerated, blend diced tomatoes, fresh basil, extra virgin olive oil, and salt and pepper to taste. Set aside until hamburgers are cooked.
Begin scooping out a small handful of ground chuck and placing the loose balls on a baking sheet. Once you have all 12 balls portioned out (roughly the same amount in each), begin forming patties by lightly pressing them down with your hands. Be careful not to overwork or compress your patties. Once flat and round, use your thumb to create a well in the center of each patty.
With a kitchen spoon, fill each of 6 wells with the Mozzarella mixture, lightly pressing in with the back of the spoon.
Place the 6 empty patties on top of the 6 filled patties and lightly press together, crimping the edges of each with your fingertips. Once all patties are crimped, you are ready for the griddle.
Grill the hamburgers for about 3 minutes on each side for medium and continue cooking a couple of minutes per side if you prefer medium-well to well-done burgers.
Toast the buns on the griddle for 30 to 45 seconds, place patties on each of 6 buns and top with spoonfuls of the fresh marinated tomatoes and basil.