I've only found answers that involve centering only one column, such as this one.
why don't you use \centering for the horizontal centering?
It's pretty ugly and I really wouldn't recommend to make this type of table (see the discussion of how to design publication-quality tables in the documentation of booktabs), but if you're sure you want to reproduce exactly your image:
Edit: Your question title talks about vertical centering, but since you say you aren't happy with the above centering, perhaps you actually wanted horizontal centering also? You can get it like this:
If that is still not what you wanted, please edit your question to be more clear about what exactly you are trying to reproduce from your figure.