adobe photoshop - How can I recreate this posterization effect?

So for the last couple of days I've been researching and trying to find out how to recreate this awesome looking effect, but haven't found any similar tutorials on the internet, and where better to ask for professional help than here.

On the left is the effect I'm going for, on the right the guy I'm trying to put the effect on.

I have an idea that the first steps is to make it black and white then apply posterize effect to 4 levels and some median filter and there is where my knowledge ends. How do I make the edges so clean and artistic, how do I colorize the picture?

Full resolution cutout: https://i.imgur.com/0FczLlE.png

Full picture of the effect: https://i.imgur.com/KCLDs31.jpg

Answer

I'd start out with the Cutout filter in Photoshop, I set it up to use 3 colour levels and adjusted the other sliders until I got the effect I liked best.

Then I coloured the image with the paint bucket, and added some extra highlights and shadows by making a selection with the lasso tool, and filling with colour.

Then I used this image as a guide to trace vector shapes with the pen tool, and filled them with colour, then disabled the raster layer.

The benefit of this method is that the image is vector, and can be rescaled without pixelization.