Prepare the Clams (if using fresh): Clean the clams thoroughly under cold water. Steam them in a pot with ½ cup water until they open (about 5-7 minutes). Remove the clams from their shells and chop the meat. Strain and reserve the clam juice.
Sauté the Vegetables: Warm the butter in a large pot over medium heat until melted. Add the chopped onion and celery, and sauté for about 5 minutes until they become soft.
Prepare the Roux: Sprinkle the flour over the sautéed vegetables, stirring continuously. Cook it for 1-2 minutes until a roux forms.
Add the Liquids and Potatoes: Slowly pour in the clam juice while stirring to ensure there are no lumps. Stir in the diced potatoes, thyme, bay leaf, and a small pinch of salt. Bring the mixture to a gentle simmer and cook until the potatoes are tender, about 15 minutes.
Incorporate the Clams and Cream: Stir in the chopped clams and heavy cream. Let it simmer on low heat for about 5 minutes to allow the flavors to meld. Take care to keep the mixture from boiling to prevent curdling.
Season and Serve: Taste the chowder and adjust the seasoning by adding salt and pepper to your preference. Remove the bay leaf before serving. Garnish with fresh parsley and serve warm with crackers or crusty bread.