Grate tomatoes on largest holes of a box grater into a large heatproof mixing or serving bowl until only the skin remains in your hand; it's okay if some slightly larger pieces of tomatoes and some skin get through, though you can discard the large pieces of skin. Add olive oil, basil, garlic, and red pepper flakes. Stir well and season with salt to taste. Set aside.
In a pot of lightly salted boiling water , cook spaghetti, stirring frequently, until al dente. When pasta has almost finished cooking, transfer ¼ cup (30ml) pasta cooking water to tomato mixture and whisk to form an emulsion.
Using tongs, transfer pasta to tomato mixture along with an additional ¼ cup (60ml) pasta cooking water. Vigorously toss and stir pasta to emulsify sauce and coat noodles. Add half of the breadcrumbs and toss to combine. The pasta should be well coated with creamy, emulsified sauce. If it seems dry, add extra pasta water and olive oil, 1 tablespoon (15ml) at a time, until it reaches the desired consistency. Taste for seasoning.
Transfer pasta to warmed plates and sprinkle with remaining breadcrumbs. Top with cheese, if desired. Serve right away.