Creating a vertical header

Hi, am having a right old time of it trying to create a vertical header in a different theme. So much so that I am looking at GP as an alternative. I am looking for not just a vertical menu, but a vertical header that consists of a logo with a vertical menu beneath it, on desktop around 300px wide, or 20% – 25% ish. The content will align to the side of the header. No additional sidebars required.

Here’s an example of what I wish to create: Great example of vertical header / menu here

If anyone can help advise me, that would be great as this has been a show stopper so far. Thanks!