In a large stockpot bring 3 cups of water to a boil. Add the clams, cover, and cook for 5 minutes. Uncover the pot and quickly stir the clams with a wooden spoon. Cover and cook 5 to 10 minutes longer (this will depend on the type and size of the clams), or until most of the clams are open.

Transfer the clams to a large bowl or baking dish and strain the broth twice through a fine-mesh sieve into a bowl, being careful to strain out the sand. (You should have about 8 cups of clam broth. If not, add enough water to bring the volume up to 8 cups.) When the clams are cool enough to handle, remove them from their shells and chop into 1/2-inch pieces. Set the clams and broth aside.

Cook the bacon in a large heavy pot over medium heat until crisp and the fat is rendered. Pour off all the bacon fat except 2 tablespoons. Add the 4 tablespoons butter, leeks, onions, and celery and cook until softened, about 5 minutes. Add the garlic, thyme, and bay leaves and cook until the vegetables are thoroughly wilted, about 3 minutes, being careful not to brown. Add the potatoes and reserved clam broth and bring to a boil. Lower the heat, cover, and simmer until the broth thickens slightly and the potatoes are very tender, about 30 minutes. (If you like a thicker broth, mash some of the potatoes against the side of the pot with a wooden spoon.) Remove from the heat, stir in the clams and cream, and season with the pepper and the salt to taste.

Set the chowder aside for 1 hour, covered, to allow the flavors to marry. Place the pot over low heat and slowly reheat, being careful not to let boil. Serve hot; garnish each bowl with a pat of butter and some parsley and chives.