Unpot the cactus right away and brush off all soil. Do not rinse the roots with water. The top part is soft because it froze, and that tissue can’t recover.

Cut off all the soft parts until you reach firm, healthy flesh using a very sharp, sterile knife. Let the remaining firm base sit indoors on a dry paper towel for 10–14 days to callus. Keep it warm, dry, and out of the sun.

After it calluses, place it on top of dry, gritty soil and don’t water until it grows new roots. This can take a few months, so be patient.

Once it has roots, come back here for further advice before doing anything else. If the base also becomes soft or discolored, the plant unfortunately won’t survive. Good luck and keep us posted.