Place a large stock pot of water over high heat and bring to a boil. While you are waiting for the water to boil, assemble the sauce.
In a large bowl, place the diced tomatoes with all of the seeds and juice. Tear or chop the basil, adding it to the bowl. Reserve a little basil for garnish. With a garlic press, press the garlic into the bowl. Add the olive oil. Taste. Season with sea salt and black pepper. Taste. Add more olive oil, sea salt, and pepper as necessary.
Once the water is boiling, season it with sea salt and add the pasta. Cook until al dente. Immediately remove the pasta, scooping it into the bowl with the tomato sauce. Stir to coat. Taste. Season with salt if necessary. Pour the pasta into a large serving bowl and grate a generous amount of ricotta salata on top. Finish with a little sprinkle of basil.