Scrub the clams under cold water to remove any sand or grit.
In a large pot, add the clams and cover with water. Bring to a boil over medium heat. Cook for about 5 minutes, or until the clams have opened. Discard any clams that remain closed.
Remove the clams from the pot, reserving 1 cup of the clam broth. Chop the clams into bite-sized pieces and set aside.
Cook the Vegetables:
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and celery. Cook for about 5 minutes, or until softened.
Add the minced garlic and cook for an additional 1 minute.
Make the Base:
Add the diced potatoes, clam juice, chicken or vegetable broth, and bay leaf to the pot. Bring to a simmer and cook for about 10-15 minutes, or until the potatoes are tender.
Thicken the Chowder:
In a separate saucepan, melt the butter over medium heat. Add the flour and cook, stirring constantly, for about 2 minutes to form a roux.
Gradually whisk in the milk and cream, cooking until the mixture thickens and is smooth.
Combine and Finish:
Add the roux mixture to the pot with the vegetables and potatoes. Stir to combine.
Add the chopped clams, dried thyme, dried parsley, salt, and pepper. Simmer for an additional 5-7 minutes, or until heated through and slightly thickened.
Serve:
Remove the bay leaf and discard.
Ladle the chowder into bowls and garnish with fresh parsley.