Heat a 12-inch skillet over a low flame. Add the extra-virgin olive oil, garlic, and crushed red pepper, if using, and gently heat until fragrant, about 1 minute. Add the onion and saute until translucent. Stir in the tomatoes, olives, capers, anchovy paste, and the vinegar. Toss to combine and cook until the tomatoes have softened and released their juices, 6 to 8 minutes. Add 2 tablespoons of the basil and toss to combine. Remove the sauce from the heat and set aside until ready to use. If not using immediately, cover and refrigerate in a nonreactive container for up to one week. Cook's Note: Bring the sauce to room temperature and then gently warm when ready to use.
Preheat the grill or grill pan over medium heat.
Brush the swordfish steaks on both sides with the olive oil and season with salt and black pepper. Grill the swordfish until nicely marked on both sides and just cooked through, about 4 minutes per side. Remove the fish from the grill and allow to rest briefly before serving.
Serve the fish hot, with the puttanesca sauce spooned over the fillets. Garnish with the remaining 2 tablespoons chopped basil, and more sauce, if desired.