Picture below. Looking for a wheel with a "deep" center (not sure if that's the right term). This pic is from a 370z, but I've seen the same look on BMWs too. Doesn't have to be the exact wheel, just the same sort of look.

 

The term is "concave".

It doesn't work on a MINI because there isnt enough room in the fender for wide wheels that are deep concave. If you want a concave wheel like the one you posted, you will need 9+ inch wheels.
It is possible to fit 9inch wide wheels in your MINI, but you will either need to run wide fenders, or have a massive amount of negative camber to make the wheels "fit" in the fender.

Of course there are wheels under 9 inch that have a very slight concave face to them, but no where as concave as those.

The Breyton GTS-R for the MINI is slightly concave. (Combfilter's R56)


Rotiform NUE is also slighly concave (Creeve's R56)

 

Unrelated to the question at hand, but I'd like like to know how Creeve made his halogens have a dark housing! I figured if you darkened the halogen housing then it wouldn't really light up in front of you.

 

I may be mistaken, but I think that's tint on the headlight lenses.

I figured that it would need to be a fairly wide wheel to get that look. 9" is too much for me. Not really interested in negative camber or wider fender wells. I do like the look of those Rotiforms. Might look closer at those.