Prepare all ingredients: clean and cut the fish into large chunks, slice leeks into rings, peel and slice carrots into rounds, and chop celery into small pieces. Mince garlic cloves.

In a large Dutch oven, melt 2 tablespoons of butter over medium heat. Add the leeks, carrots, and celery, cooking gently for 5-6 minutes until softened but not browned. Add minced garlic and cook for another minute until fragrant.

Pour in 4 cups of water or fish stock, add bay leaves, thyme, parsley stems, and season with salt and pepper. Bring to a gentle simmer and cook for 10 minutes to develop flavors.

Add the fish chunks to the simmering broth, ensuring they are mostly submerged. Cook gently for 8-10 minutes until the fish is just cooked through and flakes easily with a fork. Be careful not to overcook.

While the fish cooks, whisk together egg yolks and heavy cream in a small bowl. Temper this mixture by slowly adding a ladle of hot broth while whisking constantly.

Remove the pot from heat. Slowly pour the tempered cream and egg mixture back into the pot, stirring gently to incorporate. The broth will become silky and slightly thickened. Do not return to high heat or the eggs may curdle.

Add lemon juice to brighten the flavors. Taste and adjust seasoning with additional salt and pepper if needed. Remove bay leaves.

Serve immediately in wide bowls, garnishing with fresh parsley. Accompany with crusty bread for dipping into the creamy broth.