Fill a large stock pot with water and bring it to a boil for the pasta. While the water comes to a boil, prepare the sauce.
In a medium saucepan, heat the oil over medium heat. Add the garlic and sauté until fragrant. Right before it starts to turn color, add the wine. Let the wine bubble and cook for 3 minutes or so, to let the alcohol boil off.
Next, add the tomatoes and a pinch of sea salt. Bring to a boil, and reduce the heat to a simmer. Cook for 30 minutes, stirring occasionally. Taste and season if needed with more sea salt. Add the parsley and stir to combine.
In the last five to ten minutes of the sauce cooking, prepare the pasta. Generously salt the water, add the pasta, and cook until al dente. Once finished, scoop the pasta out of the pasta water and add it directly into the pan with the sauce. Toss the pasta to coat. Divide the pasta into individual bowls, top with equal parts freshly shaved Parmigiano Reggiano and Pecorino Romano and serve.