Fry the bacon in a cast iron skillet over medium-low heat, turning the slices once or twice with a fork. This should take 10 minutes. Drain the bacon on a paper towel-lined plate, and keep 3 tablespoons of the bacon grease. Let the bacon cool, then break into smaller pieces.
In a 6-quart Dutch oven set over medium high heat, saute the carrots, onion, and celery in the bacon grease for roughly 8 minutes.
Sprinkle the flour over the vegetables, then cook the mixture for 2 minutes, stirring with a wooden spoon.
Gradually add the clam juice, stirring continuously, then pour in the water, potatoes, thyme, bay leaf, salt, and pepper. Mix to combine.
Cover and bring to a boil, then simmer for 15 minutes, stirring every 5 minutes so the potatoes won't stick to the bottom of the pot. The chowder will start to thicken from the potato starch.
Reduce the heat to low, remove the bay leaf and thyme, then add the cream, milk, and whole baby clams. Stir gently and let the the milk and clams heat through, roughly 5 minutes. Be careful not to boil the chowder.
Remove from the heat and stir in the crumbled bacon. Reserve some for a garnish. Taste and adjust seasonings if necessary.
Serve the New England clam chowder warm with fresh parsley and oyster crackers.