I think this one is knit though Ravelry: Lucy Hat pattern by Carina Spencer. Love this hat! I've got to do this one and I'll bet I have to do it for several members of my family! It does need a nice button on that flipped up brim, though.
i think you could make this with tunisian. when it gets the the split, you could keep working half the stitches until both halves are long enough and then start stitching across the entire piece again at the other end.