Instructions:
Using 4 mm needles
Cast on 28 in black double knit
Beg K row, SS 4 rows in band colour.
Continue in SS and work 2 rows in black.
Continue in SS, but K2tog or P2tog at the start of every row until 2 stitches remain.
Pass the second stitch over the first.
B & T tightly

Brim
Cast on 45 in black
Knit 3 rows
Next row: (K1, K2tog) repeat to end
Cast off.

Alternatively, work the hat in one piece
Cast on 42 stitches and follow the brim pattern, this will leave you with 28 stitches to start the colour band.
Now follow the pattern again.
This gives an all-in-one hat and brim…..less sewing! 
Thank you to everyone who has sent me this suggestion.

Making Up:
Sew row ends together on both the crown and the brim.  Oversew the brim to the crown.