How to Make It
In a large, heavy pot, heat the olive oil until shimmering. Add the shallot, garlic and basil and cook over moderately high heat, stirring, until the shallot is translucent, about 2 minutes. Add the cherry tomatoes and cook until the skins loosen and the tomatoes soften, about 3 minutes. Stir in the wine and simmer over moderate heat until reduced by half, about 8 minutes.
Pass the canned tomatoes and their juices through a food mill into a large bowl.
Add the pureed tomatoes to the pot and bring to a simmer. Cover and cook for 40 minutes. Let cool slightly, then strain the broth through a sieve into a large bowl, pressing on the solids; you should have about 7 3/4 cups of broth. Season with salt. Rinse out the pot.
In the pot, heat the olive oil until shimmering. Add the leek, fennel, celery, oregano and crushed red pepper and cook over moderately high heat, stirring, until the vegetables have softened, about 3 minutes. Pour in the tomato broth and bring to a simmer. Add the clams, cover and cook for 5 minutes, shaking the pot occasionally. Stir in the mussels and shrimp. Season the snapper with salt and place it on top of the stew; press gently to partially submerge it. Cover and cook until the fish is just white throughout, about 6 minutes.
Transfer the fish to a large serving bowl. Season the cioppino with salt. Transfer the seafood to the bowl with the fish. Pour the tomato broth over the seafood. Garnish with parsley and serve with toasted baguette slices.