3 large rip tomatoes, cored and sliced 1/2-inch thick
2 cloves garlic, finely chopped
3 tablespoons extra-virgin olive oil, plus more for greassing the pan
1 cup coarse, fresh bread crumbs, preferably from sourdough bread
Kosher salt and freshly ground black pepper
1/3 cup finely grated Parmigiano-Reggiano
1/4 cup roughly chopped basil leaves
Place the tomato slices between 2 paper towels and let stand for 45 minutes to an hour. This will remove some of the liquid and keep the gratin from being soggy.
Preheat oven to 500 degrees Fahrenheit with a rack in the center position.
Brush a large, shallow gratin dish or earthenware casserole with a little olive oil.
Arrange the tomato slices only just slightly overlapping in the dish. Season lightly with salt and pepper and scatter half the basil over the top.
Heat the olive oil in a small skillet over medium-high heat. Add the garlic and saute only until the aroma is released, about 45 seconds.
Remove from the heat and stir in the bread crumbs and a pinch more salt and pepper. Scatter the bread crumb mixture over the tomatoes and top with the Parmigiano.
Bake for about 15 minutes, until the crumbs are golden. If desired, let stand for up to 1 hour, and reheat in a low oven for 5 to 10 minutes before serving. Just before serving, garnish with the remaining 2 tablespoons of basil.