Heat the butter and olive oil in a soup pot or Dutch oven over medium-high heat. Add the onions and cook, stirring frequently, seasoning them with the salt and pepper, until soft and translucent, about 5 minutes. Add the garlic and stir for a minute or two, to help them release their aroma.

Add the potatoes and 2 cups of water to the pot. Cover, bring to a boil then reduce the heat to a steady simmer and cook until the potatoes are tender when poked with the tip of a sharp paring knife, about 10 to 15 minutes.

Add the radish leaves and stock. Cover, bring to a boil, then reduce the heat and simmer just until the radish leaves are wilted and cooked through. Remove from heat.

If using an immersion blender, add the cream, mustard, cayenne, and cream to the pot and puree until smooth. If using a standard blender, let the soup cool until tepid then puree the soup with the cream and mustard. (Never fill a blender more than half full with hot liquid as it can blow off the lid and cause injuries.) Rewarm the soup and serve with any of the suggested garnishes.