Holding two strands of yarn together - a 4ply and a laceweight - can give you a standard DK gauge.
It can also emphasise or diffuse colours. In this case the undyed cream of the alpaca silk subdues the much brighter 4ply.
The alpaca/silk makes the hat buttery soft and gives it a slight halo.

Simple DK Hat in one strand of Choufunga 4ply and one strand Cloud 800
The other version uses one strand of a DK yarn...
This is a proper woolly hat!
I liked it so much I made one for myself last winter.
For this version I used WYS Bluefaced Leicester in the dark grey Fossil. I didn't want a fold back brim but I still wanted it to be quite deep (large forehead and lots of hair). So I knitted my brim to 8cm before starting the main body of the hat.
You can easily adapt the size or change the look of the hat:
You can knit it longer for more slouch, short for less. Keep the double brim rib or half the length for a single brim. Change the rib pattern or omit entirely.
Knit for smaller heads or larger ones. The pattern suggests subtracting or adding 12 stitches to your cast on.
If you're looking for a wee challenge, get all fancy with your cast on and try an alternating cable cast on or a tubular cast on.
Stripe, fade or colour block it. This pattern is great for stash busting and using up small amounts of yarn. You don't need much yarn to knit a hat. Raid your stash for some 4ply and a laceweight, hold the two strands together and knit them to get a DK tension.
Or find some DK weight yarn and knit with one strand of that.
For the folded brim version you'll need approx. 165m of DK or 165m EACH of a 4ply and laceweight.
So, given all those positives I thought I'd whip up another version as a quick shop sample to show off our newest yarn -
Symfonie Viva DK, a hand dyed merino superwash. I used shade Spring Blush.
I decided to do a rolled brim version. You simply cast on and start knitting. No rib. The brim will naturally roll a little.
As Viva is a variegated yarn, the colours will come together in different ways, depending on what you are making. So I wasn't quite sure what I'd get with a hat sized project. Turns out I got stripes!
But then... as I started to decrease at the crown of the hat the colours started to pool. That means as I was knitting around each colour gathered together to form blocks of colours. You can see a little of it with the block of turquoise.
I wasn't keen on this as the rest of the hat had very definite stripes. So to combat it I took back my knitting to where it started to pool and cut the yarn, leaving a tail to weave in later. I then started knitting again about half way through the next colour on the ball.
There is no science to this! I just wanted to break up how the colours were forming. There is still a little bit of pooling but I quite like it as a break before the colours form narrower stripes as the crown gets smaller and smaller.
Overall I think it looks great but if you prefer precision with your colours you might want to think about buying individual colours and striping it... manually!
Interestingly, some may find the stripes a type of pooling - when stitch count and gauge converge to form a pattern. To combat pooling, especially if you are working with more than one skein over larger projects, try striping your skeins together. This can give a more even colour distribution. I could have split my 100g ball in half and striped them together if I didn't want stripes are all. Maybe I'll try that with my leftover yarn and make some
small fingerless mitts?
This hat also has a very different feel to the fluffy and woolly versions. Superwash merino has a smooth shiny texture so this hat has great stitch definition and drape.