I have never seen "chef" associated with men and "cook" associated with women. Is this just one of those US things?
Usually hear it that way, though a man in lesser restaurants is called a cook.
Never heard it that way, either. Typically, I only hear alterations of "chef" and "cook" in reference to rank within a restaurant's kitchen. Otherwise, a cook is someone who just reads the recipes and "cooks the food," where as a chef is someone who is an artist in what they do and makes their own recipes. I've never heard those titles having anything to do with specific gender roles.
It's not really a US thing at all, since it originated in France. I'm just shocked this is not something you all study anymore. :-) it was big in the 80's "women's studies" and "feminist" classes. I'm looking for the articles, but there were hosts of jobs that a woman did at home, which demanded different titles when a man took them on outside the home as a career. cause "men are not cooks, we are chefs".
Chefs also usually manage the kitchen to some degree.
While true, it's worth noting - again, these are not my studies, i'm repeating cloudy things from my past school work 30 years ago - it's worth noting that they choose not to use "head cook" in English, but took a term "chef" from french.