Melt butter in the stockpot. Add garlic and onion, and cook, stirring frequently, until onions have become translucent, about 2-3 minutes. Stir in thyme until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute. Gradually whisk in milk, vegetable stock, clam juice and bay leaf, and cook, whisking constantly, until slightly thickened, about 1-2 minutes. Stir in potatoes.
Bring to a boil; reduce heat and simmer until potatoes are tender, about 12-15 minutes.*
Stir in cream and milk and clams until heated through, about 1-2 minutes; season with salt and pepper, to taste. If the soup is too thick, add more milk as needed until desired consistency is reached.
Serve immediately, garnish with parsley.