Peel and chop the root vegetables into one-inch cubes.
Prepare a large saucepan of salted water and bring it to a rolling boil.
Cook the celeriac for 20 minutes, the swede for 15 minutes, and the parsnips for 12 minutes.
When the timer is up, drain the root vegetables in the colander.
Return the cooked root vegetables to the saucepan and add the butter and cream cheese. Use an immersion blender or potato masher to mash the vegetables and gently reheat over low. Alternatively, pass the celeriac, parsnip, and swede through a potato ricer or blend in a food processor before mixing with the butter and cream cheese in the saucepan over low heat.
Serve the root vegetable mash topped with the chopped fresh chives and parsley, cracked black pepper, and another knob of butter.
Notes
Root vegetable cooking times (boiled as one-inch cubes)
Celeriac: 15-20 minutes
Swede: 12-15 minutes
Parsnip: 10-12 minutes
Carrots: 5-7 minutes
Sweet potato: 12-15 minutes
Tips
Add each variety of root vegetables to the boiling water in small batches to avoid the water dropping in temperature. Dumping them all in at once will lose the boil and affect cooking time.
The root vegetables are cooked when a sharp knife can be inserted easily.