To make the chile pesto, combine the chilies, red onion and anchovies in a food processor. Drizzle in olive oil until you’ve achieved a coarse pesto. Set aside.
Bring 6 quarts water to a boil and add 2 tablespoons salt. In a 12 to 14-inch sauté pan, heat the olive oil until smoking. Add garlic and cook until soft but not yet browned, about 4 to 5 minutes. Add the pesto to the sauté pan and adjust consistency with oil to form a sauce.
Cook the bucatini according to the package directions, until tender yet dente. Drain the pasta, reserving about 1/2 cup of the boiling water and add the pasta to the sauté pan with the pesto. Toss over high heat for 1 minute, adding a scant splash of the pasta water if necessary to keep the condiment from getting too “tight.” At the very end, add the basil and toss to incorporate.
Divide among four warmed pasta bowls and serve immediately.