Smoking cap is one of those Victorian "frou-frou" things. Men were supposed to wear them so the smell of smoke would not get into their clothes/hair.
I made that cap from a pattern in an 1876 Peterson's. the cap is linen and silk embroidery thread. It was a great chance to learn/practice embroidery over tissue paper; drawing the pattern on tissue paper, embroider the pattern, and the tearing out the paper.
The pattern is such a classic Greek key pattern that it's pretty timeless for 19th Cent flair.