Bring the milk, water, and salt to a boil in a large pot. Add the celery root, potatoes, and onion and lower the heat to a simmer. Cook for about 30 minutes or until fork tender.
Remove the vegetables from the milk/water mixture and place them in the pitcher of a blender or bowl of a food processor. Work in batches, if needed, and puree the vegetables until they are smooth. Add the butter and incorporate it perfectly. Taste, then add salt and pepper as needed.
Transfer to a serving bowl, garnish with herbs, and serve immediately.
Notes
Cube the vegetables all the same size so they cook evenly.Use herbs that are reflected in the dish or meat that you are serving the Celery Root Puree with.