In a large pot, melt 3 tablespoons of butter over medium heat. Once bubbling, add 1 diced onion and 2 stalks of diced celery. Sauté for about 5 minutes, stirring occasionally, until the vegetables are softened and aromatic.

Sprinkle in 1/4 cup of flour while stirring constantly to form a roux. Cook this mixture for about 2 minutes to remove the raw flour taste, ensuring it doesn't brown; it should appear golden and thick.

Gradually pour in 4 cups of chicken stock, whisking continuously to prevent lumps. Let the mixture simmer for 2-3 minutes until it thickens slightly and becomes smooth.

Add 2 diced carrots, 2 medium diced potatoes, and 1 cup of corn to the pot. Stir well, reduce the heat to medium-low, and let the chowder simmer for approximately 15 minutes, or until the vegetables are tender.

Gently stir in 1 cup of milk or half and half, increasing the heat to medium-high. Allow the chowder to come to a gentle simmer for about 3-4 minutes.

Add 1 pound of cubed halibut to the chowder, cooking for 5-7 minutes until it turns opaque and flakes easily. Season with salt and freshly ground black pepper to taste.

Turn off the heat and allow the chowder to sit for a few minutes before serving warm. Garnish with fresh herbs like parsley or dill.