Step 1

To make the celery root purée, pour the milk in a large saucepan with 4 cups water, the coarse salt, celery root and potatoes, and bring to a boil over medium heat. Lower the heat to medium-low and simmer until the celery root is tender when stuck with a fork, about 25 minutes. Drain the vegetables, return them to the pan, and toss them in the pan over low heat until they lose their excess moisture.

Step 2

Put the potatoes through a potato ricer back into the large saucepan (no need to wash it), or if you don’t have a ricer, put them whole back into the saucepan and mash them with a potato masher until they’re very smooth. Set aside.

Step 3

Place the celery root in the bowl of a food processor, add the butter and process until smooth and creamy. Scrape it into the large saucepan with the riced/mashed potatoes, stir well to combine, and season to taste with salt and pepper. (Note: The purée can be made up to 6 hours ahead. Let it cool, lay plastic film on the surface, and refrigerate. When you’re ready to serve it, heat it in the top of a double-boiler, or gently in a heavy-bottomed saucepan, stirring as you reheat it.)

Step 4

For the glazed celery, trim the bottom of each bunch of celery bunch, but leave the stalks attached. Slice the top parts off, so the attached bunches are 5 inches long, then remove tough outer stalks (there may be three or four). Save these, along with the trimmed tops of the stalk, for another use. Run a vegetable peeler up and down the exterior of the two bunches, removing the strings, then cut each lenghthwise into quarters.

Step 5

Warm the oil in a large sauté pan, skillet or braiser over medium heat. Reduce the heat to medium-low, add the celery quarters, season with salt and pepper, a cook for about three minutes, using tongs to turn the celery as it cooks so it doesn’t color. Pour in the broth, raise heat to high and bring to a boil. Adjust the heat down so that the broth is simmering steadily and continue simmering for about 25 minutes, or until the liquid is nearly gone and the celery is lightly glazed with the broth; they should feel tender when poked with a fork. You can serve the celery right away, or hold it on the stove for up to an hour and gently rewarm it before serving. Or make it ahead up to 6 hours, chill it and rewarm it gently before serving.