Sauté the Vegetables: Melt 2 tablespoons of butter in a thick-bottomed 4- to 5-quart pot over medium heat, then add the chopped onion, sliced leeks, and 5 cups of chopped celery; cook for 10 minutes, stirring as needed, until the vegetables have softened.
Add the Garlic: Stir in the minced garlic and cook for 1 minute more, allowing it to become fragrant without changing the basic cooking method.
Add the Stock: Pour in the chicken stock and add the bay leaves, then taste the liquid and season with kosher salt as needed; the amount required will depend on whether the butter and stock are salted or unsalted.
Simmer the Soup: Increase the heat and bring the soup to a boil, then reduce the heat to low and cover the pot to maintain a gentle simmer; cook for 15 minutes.
Braise the Remaining Celery: While the soup simmers, melt the remaining 1 tablespoon of butter in a separate small sauté pan over medium heat, then add the 1 1/2 cups diced celery.
Soften the Celery: Ladle 1/2 cup of the simmering stock from the soup into the sauté pan, reduce the heat to low, and simmer the diced celery for 5 to 6 minutes, until softened; set it aside.
Cool the Soup Slightly: Remove the soup pot from the heat and allow the soup to cool slightly, then remove and discard the bay leaves.
Purée the Soup: Use an immersion blender to purée the soup until smooth; alternatively, carefully transfer the soup to a stand blender in batches, filling it no more than one-third full at a time and keeping your hand firmly on the lid while blending the hot liquid.
Return the Purée to the Pot: If using a stand blender, transfer the puréed soup back into the cooking pot.
Finish the Soup: Stir in the cream and the braised diced celery, then taste and add more salt if needed.
Garnish and Serve: Serve the soup hot, finishing each serving with freshly ground black pepper and chopped chives or parsley.
