How to Make It
In a large pot of salted boiling water, cook the pasta until it's barely al dente. Drain, reserving 11/4 cups of the cooking water.
Meanwhile, in a very large skillet, heat 2 tablespoons of the olive oil. Season the salmon with salt and pepper, add it to the skillet and cook over high heat until browned on both sides but not cooked through, about 6 minutes. Transfer the salmon to a plate and pour off the oil in the skillet.
Add the remaining 2 tablespoons of oil to the skillet along with the garlic and crushed red pepper. Cook over moderate heat until the garlic is lightly browned in spots, about 30 seconds. Add the tomatoes and cook until just softened, 2 to 3 minutes. Add 1 cup of the reserved pasta cooking water and bring to a boil, gently crushing the tomatoes. Add the pasta, olives and capers and cook over moderate heat, stirring, until the liquid is slightly absorbed, about 2 minutes. Add the salmon to the skillet and break it up into chunks. Cook, tossing, until the salmon is nearly cooked through and the pasta is al dente, about 2 minutes; add more of the pasta cooking water if the sauce is dry. Stir in the basil, transfer the pasta to bowls and serve.