Place the spaghetti in salted boiling water. Stir to prevent the strands from sticking together.
While the pasta is cooking, heat up the olive oil in a saucepan and gently saute the garlic until golden. Add the tomatoes and cook until the tomatoes become soft. Season with salt.
About 2 minutes before the spaghetti is at the 'al dente' stage, drain, reserving approximately 1 1/2 cups of pasta water.
Add the spaghetti and pasta water to the saucepan. The pasta water will help lengthen and loosen the sauce. Turn off the heat. Add the torn basil leaves and cook together for approximately 30 seconds. Generously sprinkle Pecorino cheese and mix well. Drizzle with olive oil. Transfer the spaghetti to a serving bowl. Top with more Pecorino cheese and serve immediately.