Heat olive oil in a heavy-bottomed pot over medium-high heat. Add celery and cook until tender. Add garlic and sauté for 1 minute until fragrant. Stir in flour and remove from the heat.
Whisk in milk until smooth. Return to the heat, add fish stock, and bring the mixture to a boil.
Add potatoes, reduce heat, and simmer for 10 minutes or until the potatoes are almost tender, stirring occasionally to prevent sticking.
Meanwhile, brush and clean the fresh mussels under water. In a separate saucepan, add the mussels, cover, and cook over medium-low heat for 5 minutes, or until the mussels open.
Drain, remove half of them from their shells, and keep the rest in their shells. Rinse the clams, drain, and set aside.
Add the fish fillets and prawns to the pot. Cook for 5 to 8 minutes, or until the fish is firm and the prawns are pink.
Stir in all of the mussels, clams, and half of the thyme. Season with salt and ground black pepper. Simmer for 5 minutes, then turn off the heat.
Sprinkle with freshly chopped parsley and the remaining thyme. Serve immediately with toasted sourdough.
