The Italian Cast on is found on page 67 of RD KH.
I can’t find a video online for this cast on (all searches for italian cast on lead to a tubular cast on) – but I think it is just a variation that ends up the same as the long tail cast on.
It is a two strand, one needle cast one, with the first row of stitches being done with the cast on (so I worked the first row as a wrong side row). I found it VERY fiddly to work, and the first row was a bit off-kilter. It does seem to pull in a bit at the bottom (the cast on edge is slightly smaller than the knit fabric itself). It isn’t super-stretchy or especially firm. It does tend to bounce back into shape very well.