This is a simple and plain Victorian cotton day cap, such as in this Victorian painting or this 1855 painting. ‘This shape is particularly liked by the poor, from the ease with which it is made up and washed, as, upon undrawing the string, it […] lies quite flat to be ironed.’ (The Workwoman’s Guide, 1840)
The day cap is completely handsewn and made of white cotton batiste. The back of the cap is gathered on a drawstring. I very easy to iron because it’s perfectly flat when the back of the cap isn’t gathered. Here’s a ca. 1865 flat day cap with drawsting casing at the neck, and another similar day cap (apart from the ruffle).
I used a combination of running and overhand stitches to sew the cap. And I finished the raw edges with a small hand-rolled hem.