Cut the top 1/4-inch off each tomato and reserve. With a serrated knife, cut the interior membrane away from the outside skin without cutting through completely; scoop the membrane and seeds out with a spoon and transfer to a strainer set over a bowl to drain. Season the hollowed tomatoes and the membrane in the strainer with salt and pepper.
Put the onions in a small bowl and cover them with 2 tablespoons vinegar and a pinch of salt. Let stand 10 minutes; this will remove some of the raw sharp flavor of the onion. In a bowl, whisk together 1 tablespoon vinegar, the garlic oil and 1/4 cup of the drained tomato water. Season well with salt and pepper.
Coarsely chop the drained tomato membrane and put in a mixing bowl. Drain the onions and add them along with the grissini pieces. Drizzle the dressing over the bowl and toss very well; season again and add more oil, tomato water and vinegar, as needed, to evenly moisten the stuffing. Stuff each tomato with 1/4 of the stuffing and garnish with the tomato tops. Chill until ready to serve.