Put the clams and 2 cups water in a pot. Cover, bring to a boil over medium-high heat and cook 5 minutes. Uncover and continue to cook until the clams open, 5 to 10 minutes (discard any that do not open); transfer the clams to a bowl. Pour the liquid into a large measuring cup. (You should have 3 cups liquid; add water if needed.) Wipe out the pot.
Pour the liquid back into the pot through a paper towel-lined sieve. Add the potatoes, cover and simmer until tender, about 15 minutes. Remove one-third of the potatoes. Continue to cook the remaining potatoes, covered, until soft, about 10 more minutes. Puree in batches in a blender until smooth. Return the soup to the pot
Cook the bacon in a skillet over medium heat until crisp, about 5 minutes. Add the onion and celery and cook until soft, about 5 minutes. Add the garlic, thyme and bay leaves and cook, stirring, about 3 more minutes. Add the bacon mixture and reserved potatoes to the soup. Cover and cook over low heat, about 5 minutes.
Meanwhile, remove the clams from their shells and roughly chop. Stir the clam meat and half-and-half into the soup; remove from the heat, cover and set aside, 20 to 30 minutes.
Discard the bay leaves. Season the soup with salt and pepper and reheat. Serve topped with a slice of butter, parsley, chives and paprika.
TIP: When blending hot liquids, first let cool for 5 minutes or so, then transfer to a blender, filling only halfway. Put the lid on, leaving one corner open; Cover the lid with a kitchen towel to catch splatters and pulse until smooth.
Per serving: Calories 353; Fat 9 g (Saturated 4 g); Cholesterol 76 mg; Sodium 251 mg; Carbohydrate 36 g; Fiber 4 g; Protein 29 g