Fill a large stock pot with water and bring to a boil. While water is coming to a boil, peel the skin from all the tomatoes with a vegetable peeler. Slice the tomatoes in half and remove the seeds and core. Dice them very finely and place them in a large mixing bowl.
Add the garlic, olive oil, a generous pinch of salt, and chili flakes. Tear the basil with your hands into small pieces and add to the tomato mixture. Stir to combine. Taste and season with salt as necessary.
Once the water has come to a boil, season it generously with sea salt. Add the capellini and cook until al dente. When the pasta is finished, scoop it directly from the stockpot into the mixing bowl with the tomatoes. Stir to combine. Taste. Season with salt if necessary. Divide into individual bowls and finish with Parmigiano Reggiano.