In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic, chopped fennel, and diced carrot. Cook for another 5 minutes until the vegetables are softened.
Add the diced tomatoes (with their juice), fish stock, saffron, thyme, and bay leaf. Bring the mixture to a simmer and let it cook for 10 minutes.
Season the broth with salt and pepper to taste.
Add the fish chunks to the pot and simmer for 5 minutes.
Carefully add the shrimp and mussels, cover the pot, and cook for an additional 5-7 minutes, or until the mussels have opened and the shrimp are pink and opaque.
Remove the bay leaf and discard. Serve the bouillabaisse hot, garnished with fresh parsley and lemon wedges on the side.