Heat the olive oil in a large pot over medium heat. Add the onion, garlic, and fennel. Cook for 5 minutes until the vegetables soften.
Stir in the cubed potatoes, crushed tomatoes, fish stock, saffron threads, and bay leaves. Bring the mixture to a simmer.
Cook uncovered for 15 minutes until the potatoes are nearly tender. Stir occasionally to prevent sticking.
Add the fish chunks and mussels to the pot. Cover and simmer for 6 to 8 minutes until the fish flakes easily and the mussels open.
Remove the bay leaves. Taste and season with salt and black pepper. Ladle the stew into bowls and top with chopped parsley. Serve with lemon wedges on the side.