Heat 1/4 cup olive oil in a large pot over medium heat. Add 1 medium onion, diced and 2 cloves garlic, minced. Sauté until the onion is soft and translucent, approximately 5 minutes.
Stir in 1 large chopped tomato and cook for an additional 2-3 minutes until the tomatoes break down.
Pour in 4 cups fish stock or vegetable broth. Add 1/2 tsp saffron threads, 1 tsp dried thyme, and 2 bay leaves. Season with salt & pepper to taste. Allow the broth to come to a gentle simmer.
Add the prepared fish chunks and cook for about 5 minutes, maintaining a light simmer. The fish should start to flake apart gently.
Next, add 1 lb peeled and deveined shrimp and 1/2 lb cleaned mussels to the pot. Cook for an additional 3-4 minutes, or until the shrimp turns pink and the mussels open. Discard any unopened mussels to ensure safety.
Remove the pot from heat. Take out the bay leaves, and taste your bouillabaisse to adjust seasoning.
Serve hot, garnished with fresh parsley and crusty bread on the side for dipping.