I realize that my previous post did not reveal the solution in its full-fledged form. So, here goes: the White Ps are on the 7th, not the 2d. The White K cannot castle, as GP noted, because it has moved from its original square; it is therefore now on Q8, not K1. The win proceeds in several stages, as follows. Stage 1: sac the rook (SG puzzle, basic rule of thumb). Stage 2: give the opponent 4 passers (SG puzzle, ditto). Stage 3: open a Borg hyperspace conduit. Stage 4: from the Borg hyperspace conduit, reset the universal gravitational constant to 0.94 of its current value. Stage 5: under-promote the two White pawns (on the 7th, not the 2d) to knights. Proceed to mate with 2 knights. This should take no more than 47 moves in total. Stage 6: while exiting the Borg hyperspace conduit, collapse the 47 moves (as explained above) via Lorenz Transformation (physics 101) to two moves. Hey, presto!
(PS: in the position with a Black bishop instead of a knight, 1. K-Q2/K2/B2 fails against BxP, since Q-R1+ leaves Black an exit square via N6; fails in 2 moves, that is. However 1. R-R3 does win in two moves as follows: either 1. ... BxP; 2. R-R3 mate, or 1. ... K-R8; 2. R-R3 mate)