Bring a large stockpot of water to a boil and salt it generously.
In a large Sauté pan over medium heat, add the sauce and reduce to about ¼ to further concentrate the flavor.
Once the water comes to a boil. Cook the pasta about 80% of the way. Just shy of al dente
Reserve about ½ cup of the pasta water before draining.
Add the spaghetti to the sauce. Add a few tablespoons of the pasta water to the sauté pan and toss to coat. Adding more pasta water as needed.
When the pasta is cooked to al dente, remove the pan from the heat and stir in the butter, cheese and 1-2 tablespoons of olive oil plus the sliced basil.
Toss to combine, emulsifying the butter, cheese and olive oil with the sauce.
Serve garnished with additional freshly grated Parmigiano-Reggiano cheese.