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Step 1
Place 2 quarts cold water in a large pot.
Step 2
Trim the top stalks (if present) and bottom roots from 1 medium celery root. Peel the remaining skin from the celery root with a vegetable peeler or sharp knife. Halve the celery root, then cut crosswise into 1/3-inch-thick slices. Stacking a few slices at a time, cut lengthwise into 1/2-inch-wide matchsticks, adding them to the pot of cold water as they are cut to prevent them from turning brown.
Step 3
Peel 1 1/2 pounds Yukon Gold potatoes, cut into 3-inch chunks, and add to the pot. Add 3 peeled garlic cloves, 2 tablespoons kosher salt, and 1 bay leaf to the pot. Bring to a boil over high heat. Reduce the heat to medium-high and simmer, stirring occasionally, until a paring knife goes easily into the potatoes and the celery root is tender, 10 to 15 minutes. Meanwhile, place a heatproof colander in the sink. Place 5 tablespoons unsalted butter in a small microwave-safe bowl and microwave until melted, about 40 seconds. (Alternatively, melt the butter on the stovetop.)
Step 4
When the vegetables are ready, scoop out 1 cup of the cooking liquid. Drain the vegetables through the colander and let sit for a minute to let some of the steam dissipate. Discard the bay leaf, then pass the vegetables through a food mill back into the pot, or return the vegetables to the pot and mash with a potato masher until smooth. (Do not use a ricer, which will not break down the celery root very well.)
Step 5
Add the melted butter and stir to combine. Stir in the reserved cooking liquid a little at a time to achieve a loose, creamy mash (about 1/2 to 3/4 cup). Season with 1/4 to 1/2 teaspoon freshly grated nutmeg and a pinch of cayenne pepper. Taste and season with more kosher salt and cayenne if desired.