Scott wrote:

Following my previous thread about painting an MDF shelf, all of the
preparation went to plan. I used oil-based primer and full undercoat.
I am now applying [oil based] eggshell as the topcoat.

However, even after about four coats, the topcoat remains uneven.

Spray gun or short pile roller

https://www.youtube.com/watch?v=NvAZYYwpNXA
https://www.youtube.com/watch?v=htrEiKrD7AY