An Interesting Insertion by Sebastiano Tronto (and a More Interesting One by Mirek Goljan)

Scramble: R2 L2 D2 F2 D’ R2 U’ B2 D’ F2 U2 F’ D2 L’ F U B F2 U2 F2 L
Solution: U2 F B’ L2 D2 F’ U F2 L’ B2 L F2 L’ B’ L’ D L B’ D L U L’ D’ L U2 R F2 R’ L2 B (30 HTM)

Explanation: (with my NISS notation, moves in brackets are done on inverse scramble)
U2 F B’ L2 D2 //2 2x2x1 (5/5)
(B’ L2 R F2 R’ F) //All but 4 edges and 4 corners (6/11)
Final Skeleton (for normal scramble):
U2 F B’ L2 D2 F’ * R F2 R’ L2 B

* = U + L’ B L’ D L B’ L # U’ //4 edges (9/20)
+ = F2 L’ B2 L F2 L’ B2 L //1 corner, 3 moves cancel (5/25)
# = L’ D L U L’ D’ L U’ //3 corners, 3 moves cancel (5/30)

The interesting insertion is obviously the first one: it is a conjugate [U L’ B L’, D]; it works like this: setup all 4 edges to be cycled on the same face (as well as the 4 unsolved corners), cycle them with a single move, undo setup.
As Mirek cleverly noticed, with this technique you can solve all the 8 pieces at the same time (since the 4 corners are also a single 4-cycle):

“In that case, to make it even more interesting (and less work), you can solve all 4 edges and 4 corners with “one move U” and, well, some more (9+9) preparation moves like this:
* = B D R2 B R’ B2 D U2 F’ _U_ F U2 D’ B2 R B’ R2 D’ B’
It is still 30 move total, though.”

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