Preheat the oven to 400 degrees F. Line a small rimmed baking sheet with parchment paper.
Heat 2 tablespoons of the olive oil in a medium nonstick skillet over medium-high heat until it starts to shimmer. Sprinkle the halibut with some salt. Sear the halibut on both sides until lightly golden, about 2 minutes per side. Transfer the halibut to the prepared baking sheet lined and bake in the oven until the internal temperature reaches 130 degrees F on an instant read thermometer, 5 to 6 minutes.
Return the skillet to medium-low heat. Add the remaining 2 tablespoons olive oil. Cook the onions and garlic until slightly softened, about 2 minutes. Add the anchovy paste, olives and capers to the skillet and stir to combine. Add the crushed tomatoes and crushed red pepper flakes and bring to a low simmer for 5 minutes. Add the wine and simmer until the wine cooks off slightly, about 2 minutes. Season with salt.
To serve, spoon the sauce directly onto the plate and top with the halibut filets. Top with the basil and lemon zest.