This is a simplified version of the classic Italian seafood stew. The vegetable base can be made ahead of time and frozen. When ready to serve, simply thaw and stir in the fish, crab, shrimp, and clams to finish cooking.
Heat oil in a large pot over medium heat. Add garlic, red pepper flakes, onions, fennel, and bell peppers and cook until softened and onions and fennel are translucent. Stir in tomatoes with their liquid, broth, wine, tomato paste, oregano, and thyme and bring soup to a boil. Reduce heat to medium-low, cover, and simmer for 25 minutes.
Meanwhile, brush baguette slices all over with oil then arrange in a single layer on a large baking sheet. Bake, flipping halfway through, until toasted and golden, 8 to 10 minutes; set crostini aside.
Stir fish and crab into pot with broth mixture and simmer for 5 minutes. Add shrimp and mussels, cover, and simmer until shrimp are just cooked through and mussels have opened, about 5 minutes more. (Discard any unopened mussels.)
Stir in basil, salt, and pepper then ladle into bowls and serve with crostini on the side.