This pattern can be found in my 2016 book Double or Nothing: Reversible Knitting for the Adventurous.
Double-knitting and entrelac are really made for each other. Don’t believe me? Try this pattern. I’ve never liked the back of single-layer entrelac, so I vowed that I would, at some point, try to do it in double-knitting. There are a bunch of issues with this, and I think I’ve found elegant solutions for them all.
There’s a fascinating trick to this pattern: if you’ve ever done entrelac in the round with more than two colors, you’ll know that the color changes happen in concentric rings as you approach the crown. In this pattern, the color changes appear to move radially instead. How? You’ll have to find out.
For a small (medium, large) hat, the brim will be 17.5 (20, 22.5)” in circumference. The rest of the hat is meant to be slouchy so it’s hard to measure brim-to-crown distance in any meaningful way. Approximately 34 (39, 44) g each of Colors A & B and 22 (26, 29) g each of Colors C & D will be needed — so no matter which size you want you should have no problem using only 1 skein of each color.