I made this using 2 strands of 8ply held together.

MAIN HAT:
In blue, with 5mm hook:
R1: Magic ring with 8 HDC (Half-Double Crochet)
R2: HDC increase in every stitch (Total of 16 stitches by the end of the round)
R2: HDC, HDC increase until the end of the round (24)
R3: 2HDC, HDC increase until end (32)
R4: 3 HDC, HDC increase until end (40)
R5: 4 HDC, HDC increase until end (48)
R6: 5 HDC, HDC increase until end (56)
R7: 6 HDC, HDC increase until end (64)
R8: 7 HDC, HDC increase until end (72)
R9: 8 HDC, HDC increase until end (80)

Around these rows is the bit where you’re trying to get the sizing right. Do less or more increase rows for heads that are weird sizes.
I do a few more increases on a later row (up to a stitch count of 84), ‘cause it was feeling a little snug (I have big hair.)

R10-12: HDC until end (80)

Change colour to white:

R13: HDC until end (80)

Change colour to red:

R14: HDC until end (80)

Here’s where I realised it was going to be a tad too tight. If your sizing is fine, don’t worry about increasing here, just repeat R14 and your end of round stitch count will be 80 for the rest of the hat.

R15: 19HDC, HDC increase) until end (84)
R16- 19: HDC until end (84)

Change colour to white:
R20: HDC until end (84)

Change colour to blue:
R22-22: HDC until end (84)

Change to white, and to 6mm hook:
R23: HDC until end (84)
R24: Front post HDC, Back post HDC until end (84)

Repeat R24 until the brim is as wide as you like, or until your hands are too stiff that you rage quit. I did 6 rows.

WHITE CIRCLES:
With one strand of white, and a smaller hook (I used 3.25mm):

R1: Magic ring with 6SC (Single Crochet)
R2: SC increase in each stitch (12)
R3: SC, SC increase until end (18)
R4: SC, SC increase until end (24)

I think size and number to make will depend on the sizing of your overall hat and personal preference. I made 7 circles of this size. I spaced them evenly around, which meant I had a gap of around 7stitches between each.

ASSEMBLY
Pin circles around the brim to ensure satisfactory positioning. Attach them using your black star embroidery. You could also sew them on first, and then embroider over, or use a felting needle to stab them down. I didn’t though.

Make a pom pom. I hate making pom poms. Attach it to the top.

If it’s for a gift, weave in ends. If not, consider the possibility that the tails offer additional insulation.