Wash and scrub the clams to get rid of the dirt. Set the littlenecks aside in the refrigerator, and combine the cherrystone clams with the water, garlic, and bay leaves in a large pot. Cover, and steam over medium-high heat until the clams have all popped open, about 15 minutes. Check every 5 minutes to pull out the clams that have opened (some take longer than others), and give the pot a stir. Pull the opened clams out of their shells and chop them roughly. Cover them and set aside. Pour the broth into a big bowl through a strainer that you've lined with cheesecloth, just in case there is leftover sand; set the broth aside.
Rinse out the pot and melt the butter over medium heat. Add the pancetta, celery, onion, and thyme. Sauté this together for 5 minutes, until the vegetables soften. Sprinkle the flour into the pot; stir and coat everything well. Gradually pour in the strained clam broth, whisking constantly to break up any lumps of flour. When all the broth is incorporated, fold in the potatoes, and bring to a boil, stirring constantly for about 15 minutes. The soup will start to thicken from the potato starch.
Toss in the littleneck clams and cover the pot to let them steam open, about 5 minutes. Reduce the heat to low and fold in the chopped clams, cream, and milk. Season the soup with many turns of freshly ground black pepper and stir everything together to heat through, but do not let it boil. Serve this in nice big bowls with some chives and Parmesan Oyster Crackers.