@Tortephant , it's a really good brand and some of mine were Toast collaborations. MHL and YMC have done collaborations too, and Plumo sometimes sells them.
When I wear one of the pairs (Toast Jade, see image) someone will say how nice they are, and I've had them for years. Mine have kept their shape and the soles look almost as good as new. They're based on the Astronaut boots.
Basically they are what DMs were before DM became a fashion brand.
They are classics.
As for the 'sole of air' name, Grenson is from 'William Green & Son'.