Heat the extra-virgin olive oil in a large skillet over medium-low heat.
Add the finely minced onion and cook, stirring occasionally, until translucent, about 4–5 minutes.
Add the canned tomatoes with their juice to the skillet and crush them gently with a wooden spoon.
Season the sauce with most of the basil leaves (reserve a few for finishing), cover, and simmer on low for 15 minutes, stirring occasionally, until creamy but still slightly chunky.
While the sauce simmers, bring a large pot of lightly salted water to a boil and cook the bucatini according to package directions until al dente; drain 2–3 minutes before the maximum time for firmer pasta if desired, then reserve some pasta water.
Remove the sauce from the heat, stir in the remaining basil leaves, and season with sea salt and black pepper to taste.
Toss the drained bucatini into the skillet with the sauce, mixing to coat; add a splash of reserved pasta water if needed to loosen the sauce, drizzle with a little extra-virgin olive oil, and serve.