That guy is a real man's man.
That guy is a real man among men.
If you're a man's man, keep your promises.
His action was truly the decision of a man's man.
He can truly be called a man among men.
漢 read かん is the ordinary on-reading meaning 'China' or used in compounds like 漢字, while 漢 read おとこ is a completely different slang usage praising a manly man.
The kanji 漢 originally refers to China or the Han dynasty. Its use as slang for a 'real man' likely comes from the idea of a strong, heroic figure, possibly influenced by historical or fictional Chinese warriors. The reading おとこ is an irregular kun-reading applied to this kanji in this specific slang sense.