Wash, peel and halve the celery root. Cut it into small cubes.
Next, peel and chop 1 clove of garlic and 1 onion into small pieces.
Put everything in a pot and add cream and whole milk until everything in the pot is covered.
Place fresh thyme sprigs in a tea strainer so that it doesn't get dispersed in the mixture - just the flavor.
Bring to a boil, stirring regularly, and lower the heat.
Let it simmer for about 20 minutes until everything is completely tender.
The key for me to getting a good puree is the following:
Drain the liquid (save it in a jug/container) and (immersion) blend the tender vegetables with a bit of the cooking liquid and butter.
Add a little liquid at a time until you are satisfied with the consistency. It should be fairly thick and smooth.
Taste the puree and season with salt (possibly white pepper) until you are happy with the flavor.
Transfer the puree to a new (and clean) pot and warm it over low heat for a few minutes.