Melt the butter over medium-low heat in a heavy-bottomed large saucepan. Add the flour and whisk until completely incorporated. Cook, whisking continuously, until the mixture turns from white to blond, about 5 minutes.
Add the onions, celery and bell pepper. Cook, stirring occasionally, until the onions are translucent, about 5 minutes. Stir in the thyme and bay leaf and cook 1 minute more.
Add the broth and bring to a boil. Stir in the white potatoes and white sweet potatoes and let the liquid return to a simmer. Reduce the heat to medium-low so the liquid simmers and cook until the potatoes begin to soften, 5 to 7 minutes.
Stir in the clams and coconut milk. If using frozen and canned clams, add the frozen first, then allow the soup to simmer again before adding the canned clams. Bring the soup back to a simmer and add salt and pepper to taste. Remove from the heat, discard the bay leaf and garnish with parsley.