Preheat the oven to 355°F (180°C).

Line a baking tray with parchment paper. Place the fish, tomatoes, shallots, garlic, and chili on the tray. Drizzle the vegetables with olive oil, and season with salt and black pepper. Bake for 25 minutes.

Once done, blend the tomatoes, shallots, garlic, and chili. Add the butter and a bit of olive oil, and blend until smooth. Transfer the sauce to a wide pan, adding 1/3 cup (80 ml) of the pasta cooking water. When the sauce boils, stir in the pasta and cook for 3 minutes.

Plate the pasta, top with pieces of the fish, and garnish with black pepper, basil leaves, and a drizzle of olive oil.