Fill a container with some water seasoned to taste with lemon juice. Working root by root, peel the roots and place them in the water with to prevent oxidization. When the burdock is peeled, remove the roots from the water and slice thinly.
Preheat the oven to 250. Put the chopped burdock and cream into a small, non-reactive saucepot and bring the mixture to a simmer, seasoning lightly to taste with salt and white pepper. Transfer the pot to the oven and bake, covered, until the burdock is tender, about 30-45 minutes.
Next remove the burdock and cream from the oven, then puree in a blender, adding a little water if necessary to thin the mixture and obtain a smooth puree. Pass the burdock cream through a strainer and reserve until needed. The burdock puree can be made a day or two ahead of time, it can also be frozen and reheated, although it may need to be pureed again since freezing can cause it to separate.
To cook the potatoes, heat a pot of lightly salted water. Peel the potatoes and add to the pot, cook the potatoes for 15 minutes, or until tender. Remove the potatoes and pass through a ricer. Add the reserved burdock cream and the butter to the potatoes and stir to combine. Taste the potatoes for salt and pepper and adjust if needed. Transfer the potatoes to a serving dish and keep warm, covered, until needed.
Serve the potatoes topped with a little knob of butter, and some sliced chives, if using.
Notes
These are excellent with meat and fish. At The Salt Cellar, I serve a variation of this with our sea scallops-a play on the burdock's "oyster" flavor.