Even though I'm married, when my wife goes out of town I have to eat my own "bachelor cooking". "Living as a bachelor" is a common phrase in the US - even to describe married men who are temporarily without their spouses. If 남자의 요리 is an expression that means "the kind of cooking that men typically do", then "bachelor cooking" would be an accurate idiomatic translation.
I don't know that I'd say it's common. I've only heard reference to "living as a bachelor" in old movies (and TV reruns from the 60s or earlier, and never in real life. Also, I do remember being at a party around 15 years ago with mostly people in their 20s and 30s, and this older guy mentioned how the expectation of cooking skills had totally changed, then he polled everyone within earshot to prove his point and sure enough, all the men cooked and almost none of the women did. (I do think that's changed again cuz i feel like most of the 25-35 year olds I know (male, female, or otherwise) have an interest in cooking)
You're way overthinking this. Unless this is an idiomatic phrase that I'm unfamiliar with as a non-native (I doubt an idiom would be this basic, as it could too easily be misinterpreted), it simply means "a man's cooking." It could be anything from a world class French chef to a homeless man grilling shoe rubber over a burning trash barrel.
Let us shed tears for the plight of patriarchally raised men that aren't expected to learn life skills that are demanded of women. I wasn't raised to have any worthwhile cooking skills, I regret it but it's a self perpetuating cycle. You definitely don't want my man meals. Although I'm a great barista.