Here's a method Creating Funny Big Head Characters in Photoshop | 10Steps.SG
I second photoshop, or GIMP if you are in a crunch and doubt you will use the program much after this. We used to use it to make decals for our company trucks and we had a big cartoon character as a mascot/logo.
Clip Studio is an amazing piece of software, if your focus is drawing and painting. It also can do vector paths, but I don't think it would be the right choice for this particular work. Clip Studio is more like Photoshop.Yea I was told to try Affinity so I dled the trial version.
Also clip studio which is on sale right now.
There are some videos on Youtube of how to do it with PS but they say Affinity is better than PS when doing this type of stuff. Will have to watch some videos later to see. Affinity isnt that expensive at least. It looks like Affinity bought drawplus and discontinued it more or less.