In a large saucepan or Dutch oven, melt 2 tablespoons (30 ml / 1 fl oz) of the butter or heat the oil over medium-high heat.
Add the chopped shallots and cook, stirring occasionally, until soft and translucent, about 5 minutes.
Add the washed parsley to the pot and cook, stirring, until it is completely wilted, about 3 to 5 minutes.
Pour in about half of the vegetable stock and bring to a brief simmer, then turn off the heat.
Carefully purée the soup using an immersion blender directly in the pot until smooth. Alternatively, let the mixture cool slightly before transferring it to a standard blender and blending until velvety. (Caution: Blending hot liquids can be dangerous).
Return the puréed soup to the pot over medium heat.
Stir in the remaining vegetable stock and the cream.
Heat gently until warmed through, but do not boil.
Season generously with salt and freshly ground black pepper to taste. Just before serving, stir in the remaining 1 tablespoon (15 ml / 0.5 fl oz) of butter or oil for extra richness.
Serve immediately.