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Step 1
Use a swivel peeler to remove the brown celeriac flesh. You may need to use a paring knife to slice off small areas that you can't reach with the peeler. Rinse off each peeled celeriac, and cut into cubes.
Step 2
Add the celeriac, shallots, and whole garlic cloves to a pot or Dutch oven. Pour in enough vegetable broth to just cover the veggies. Bring to a boil over high heat, cover, reduce heat to low and cook for 20 minutes, or until the celery root is fork-tender.
Step 3
Carefully drain most of the vegetable broth (about 2/3 of it; leave some for flavor). Return the pot with the veggies back to the stove and add the whole milk and butter. Cook for 2-3 minutes over medium heat, stirring well, until the butter is melted and the milk is warmed (but not boiling).
Step 4
Carefully transfer the mixture to a blender. Depending on the size of your blender, you may want to do it in batches to prevent overheating/splattering. Blend for ~1-2 minutes, until smooth. Alternatively, you can use a potato masher and mash the celeriac right in the pot. It will still taste delicious but won't have as creamy of a texture as it does when you blend it.
Step 5
Taste and adjust seasonings as desired. Serve with more butter, salt, pepper, and fresh herbs.