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.

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.

Carefully drain most of the vegetable broth (about ⅔ 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).

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.

Taste and adjust seasonings as desired. Serve with more butter, salt, pepper, and fresh herbs.