Melt the butter in a large nonreactive saucepan. Add the onions and cook over moderate heat, stirring occasionally, until softened, about 8 minutes. Add the potatoes, fennel, carrot, fish stock and half-and-half, reduce the heat to moderately low and simmer gently until the vegetables are tender, about 15 minutes.
Strain the stew into a bowl; set aside 1 1/2 cups of the vegetables. Transfer the remaining vegetables along with 2 cups of the liquid to a blender or food processor and blend until smooth. Return the puree to the saucepan and stir in the reserved vegetables and liquid.
In a medium skillet, cook the bacon over moderately high heat until browned and crisp, about 8 minutes. Transfer to paper towels to drain.
Rewarm the stew over moderate heat. Add the oysters with their liquor and the bacon and cook until the oysters are just firm, 2 to 3 minutes. Season with salt and pepper and stir in the parsley. Transfer to shallow soup plates and serve at once.
The stew can be refrigerated for up to 1 day.
This light shellfish stew, thickened with pureed vegetables and flavored with bacon, is especially good with the dry Veuve3 Clicquot La Grande Dame.