This problem was composed by Siegfried Hornecker and published in the online magazine MatPlus, Winter 2009.
A skilled problemist will probably spot the first move within seconds, but the real challenge is in finding all of Black’s various defenses and the replies to them. (Like with pretty much all compositions, the first move is neither a check nor a capture.)
When you solve this, do give your solving path; I’m interested to find out how different people approach this!
(As a reminder, part of the point of compositions is that they explore positions that don’t naturally come up in games and illustrate interesting ideas. Saying “well in a real game Black would have resigned ages ago” or “well in a real game I wouldn’t bother looking for the shortest mate, just one that’s reasonably quick” is missing the point.)