Add the olive oil to a Dutch oven and add garlic. Cook over medium heat until small bubbles start to form around the garlic, about 2 minutes. Add the fresh basil, and cook for about 1 minute, or until very fragrant.
Add the marinara sauce, then fill the jar halfway with water, shake it to get every last drop out, and add that water to the pot. Add a generous pinch of salt and bring to a boil.
Once boiling, remove and discard garlic cloves, then add pasta and reduce heat to a simmer. Cook, stirring often, and adding a splash of simmering water as needed until the pasta is al dente, about 10 to 12 minutes.
Serve topped with Parmigiano-Reggiano and a drizzle of extra-virgin olive oil.