Heat 2 tablespoons of the olive oil in a large skillet or saucepan and cook the onions and garlic until very tender, 6 to 8 minutes. Add the tomatoes, olives, raisins, white wine, capers, and crushed red pepper flakes and cook until the tomatoes have broken down slightly and the sauce is slightly thickened, 7 to 10 minutes. Add kosher salt and black pepper, to taste, and set aside to keep warm.
Bring a large pot of salted water to a boil and cook the pasta according to package directions until just al dente. Drain the pasta, reserving 1/2 cup of the cooking liquid, and place the pasta in a large mixing bowl along with the hot pasta sauce and the basil. Toss to combine, adding pasta cooking water 1 or 2 tablespoons at a time to thin the sauce, if necessary. Serve the pasta in shallow bowls, drizzled with the remaining olive oil and garnished with the feta cheese.