From what I can tell of history cooking was a job that all cultures shared nearly equally between men and women - except for a short time in the 1950s when Americans called it a woman only task.

Note that individual families didn’t always share equally. Often one partner was better than the other, or the realities of how their family situation worked made one partner the better choice. However there was not gender/sex linked reason for any choice. (even the 1950s you could argue it was a primarily a woman only task because the reality of men expected to work outside the house while woman stayed home meant the reality of the situation - Men often would cook for parties held in the backyard)

Nearly all cultures had a concept of the men (and sometimes woman) going off alone for long enough that they would need to cook without the other sex. Most common this was war, but there were also religious gatherings that were sex segregated in some cultures.

Men’s work and Women’s work did exist in most cultures. However cooking never seems to be part of that.