Scrub and peel the celery roots with a vegetable peeler or paring knife. Trim the ends and any brown pockets; the peeled flesh should look pale and clean.

Grate the celeriac through the large holes of a box grater or food processor grating disc. Aim for strands similar in thickness so they soften evenly.

Heat a wide skillet over medium heat and melt the tallow until glossy and fluid, but not smoking. Add the grated celeriac and sprinkle with sea salt.

Sauté over medium heat for about 10 minutes, turning the shreds now and then until they bend easily rather than snap. Lower the heat to medium-low and spread the celeriac into an even layer.

Cook undisturbed until the bottom is golden brown, about 10 minutes. When the edges look set and the layer releases with a thin spatula, turn it in wide sections. Brown the second side, about 5 minutes, until the centers are tender. Serve hot.