In a very large pot, bring 5 quarts water and 3 tablespoons salt to a boil. Add the pasta and cook until just al dente, about 1 minute less than the package directions. Occasionally give the pasta a stir so it doesn’t stick together. Scoop out and reserve 1 cup of the pasta water before draining the pasta.
Meanwhile, put a large skillet over medium heat. Add the olive oil and bacon and cook until almost crisp, about 3 minutes. Don’t drain off the bacon fat. Add the garlic and cook for about 30 seconds, making sure it doesn’t get too brown. Add the tomatoes and increase the heat to medium-high.
Add the pasta and reserved pasta water to the pan, stirring the noodles into the sauce. Remove from the heat and stir in the Parmesan, basil, and extra-virgin olive oil. Taste and adjust the seasoning, adding salt and pepper as needed. Serve immediately.