In an 8-quart soup pot, sauté the bacon over medium heat until lightly browned and the fat has rendered. Remove the bacon and all but 2 tablespoons of bacon fat from the pot.
Melt the butter in the same pot, then stir in the potatoes, onion, celery, leek, and garlic. Add as much salt and pepper as you like. Increase the heat to medium-high and cook, stirring a few times, until the potatoes, onion, and celery are crisp-tender, about 10 minutes.
While stirring constantly, sprinkle the flour over the mixture. Cook for 5 minutes, stirring frequently to prevent the vegetables from sticking. Add the milk, clam juice, reserved bacon, and thyme. Bring to a simmer over medium heat and cook until the potatoes are tender about 20 minutes.
Add the cream, clams and their juice, and parsley. Bring back to a simmer and cook for 5 minutes more. Serve hot. Let any leftover soup cool to room temperature, then refrigerate, tightly covered, and serve the next day. Do not freeze.