While the water comes to a boil, start the sauce: Heat the oil in a 12-inch skillet over medium heat. Add the sausage and cook until it begins to brown, about 7 minutes. Remove and set aside.
Add 2 tablespoons of the salt and bring back to a rolling boil. Add the pasta and cook until al dente according to package directions.
While the pasta cooks finish your sauce. Add the tomatoes to the skillet and cook until they begin to burst, about 6 minutes. Add the garlic and cook until pale golden, about 2 minutes. Add the sausage back to the skillet with its drippings and toss the mixture together.
Add the pasta directly to the skillet and toss, adding in ¼ cup of pasta water or more (up to 1 cup) as needed to loosen up the sauce. Add in the Pecorino cheese and toss again. Season with salt and pepper.
Plate in bowl and top with basil. Pass Pecorino at the table, if desired.