Traditional Rope Coiling
Notes and Resources:
There is a large family of related but slightly different rope coiling techniques, which collectively I'm calling "traditional" coiling in the sense that they're widely preferred by practitioners of Japanese-derived rope styles.
There are (at least) three different ways of forming the coil -- folding, figure 8, and figure 8 with a single fold at the end -- as well as two different general approaches to finishing the bundle: by tucking the bight under the securing wraps, or by passing the bight through the end of the bundle.
Each combination provides a somewhat different compromise in terms of coiling speed, uncoiling speed, security, tangle-resistance, and bundle aesthetics. Which one is right for you comes down to personal preference.
I recommend starting with the technique Giotto demonstrates here.
A slightly more popular variation, which is less secure but faster to undo, is to use the figure-8 bundle as Giotto shows, but finish the tuck with a bight, as shown here by TwistedView.
You can see an example of the through-the-bundle finishing method here.
Erin Houdini has an interesting variation on Kink Academy, if you have an account there, as well.