In a large pot or Dutch oven over medium heat, cook the diced bacon until it becomes crisp and brown. Use a slotted spoon to remove the bacon bits and set them aside on a paper towel, leaving the rendered fat in the pot.
Add the butter to the bacon fat in the pot. Once melted, stir in the onion and celery. Cook until the vegetables are soft and translucent, which should take about 5 to 7 minutes.
Sprinkle the flour over the cooked vegetables. Stir constantly for about 2 minutes to cook out the raw flour taste. This will form a thick paste that helps thicken the soup later.
Slowly whisk in the reserved clam juice from the cans. Add the cubed potatoes, thyme, and the bay leaf. Bring the mixture to a gentle boil, then reduce the heat to low. Cover and simmer for 15 to 20 minutes, or until the potatoes are tender when pierced with a fork.
Stir in the heavy cream, half-and-half, and the chopped clams. Let the soup heat through for about 5 minutes, but do not let it reach a hard boil, as this can cause the cream to separate or the clams to become rubbery.
Remove the bay leaf. Season with salt and black pepper to taste. If the chowder is too thick, you can add a splash more milk or broth to reach your desired consistency.