Step 1: Dice the bacon or salt pork into small pieces. In a large, heavy-bottomed pot or Dutch oven, render the bacon/salt pork over medium-low heat until crispy. Remove the crispy bits with a slotted spoon and set aside on a paper towel-lined plate for garnish. Leave about 2-3 tablespoons of rendered fat in the pot, discarding any excess.
Step 2: Add finely diced yellow onion and celery to the pot with the rendered fat. Sauté over medium heat, stirring occasionally, until softened and translucent, about 5-7 minutes. Do not brown.
Step 3: Sprinkle the all-purpose flour over the softened vegetables. Cook, stirring constantly, for 1-2 minutes, forming a roux. Ensure the flour is fully incorporated and cooked to prevent a raw flour taste.
Step 4: Slowly whisk in the clam juice and whole milk. Whisk continuously to prevent lumps from forming. Bring the mixture to a gentle simmer, stirring frequently, until it begins to thicken slightly.
Step 5: Add the cubed potatoes, bay leaf, fresh thyme, salt, and black pepper. Bring the chowder back to a simmer, then reduce the heat to low, cover, and cook for 15-20 minutes, or until the potatoes are tender when pierced with a fork. Stir occasionally to prevent sticking.
Step 6: Gently stir in the drained chopped clams and heavy cream. Heat through for another 3-5 minutes, being careful not to boil the chowder once the cream is added, as it can curdle. Taste and adjust seasonings as needed.
Step 7: Remove the bay leaf before serving. Ladle the hot clam chowder into bowls. Garnish generously with the reserved crispy bacon/salt pork bits, fresh chopped parsley or chives, and a handful of oyster crackers. Serve immediately.