An Expert 11×11 Puzzle Solved with Forced Chain in 23 Steps

This 11×11 board rates as expert (difficulty score 1126). Solving it from scratch takes 23 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, marking A1 would force B10, B11, C2, and 6 more cleared (together, two regions have open cells only in columns B and C), then D4, D5, D6, and 5 more cleared (every open cell left in this region sits in column D, so its marker has to land there), then E9 (the last open cell in region 10), and the chain continues, and then region 7 would be left with no open cell for its marker. So A1 can't be the marker there.
2. Next, if B1 were the marker, it would force C3, C4, C5, and 3 more cleared (together, two regions have open cells only in columns A and C), then D4, D5, D6, and 5 more cleared (every open cell left in this region sits in column D, so its marker has to land there), then E9 (the last open cell in region 10), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
3. Then, that one can't be the marker: at C1 it would force D3 (the last open cell in region 2), then F2 (the last open cell in region 3), then E5, E9, E10, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), and the chain continues, and region 8 would be left with no open cell for its marker.
4. After that, if E1 were the marker, region 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
5. Now, that one can't be the marker: at A2 it would force B10, B11, C3, and 5 more cleared (together, two regions have open cells only in columns B and C), then D4, D5, D6, and 5 more cleared (every open cell left in this region sits in column D, so its marker has to land there), then E9 (the last open cell in region 10), and the chain continues, and column B would be left with no open cell for its marker.
6. From there, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
7. Following that, together, two regions have open cells only in columns A and C; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
8. First, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
9. Next, place a marker at E9. Region has exactly one open cell left. Placing here clears the rest of row 9, column E, and its region. Placing here also clears its 2 touching neighbours.
10. Then, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 2 touching neighbours.
11. After that, place a marker at C8. Column 3 has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region.
12. Now, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
13. From there, every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
14. Following that, every remaining candidate in this region touches G2 and H2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
15. First, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
16. Next, place a marker at A4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region. Placing here also clears its 2 touching neighbours.
17. Then, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
18. After that, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
19. Now, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
20. From there, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
21. Following that, place a marker at I11. Region has exactly one open cell left. Placing here clears the rest of row 11, column I, and its region. Placing here also clears its 1 touching neighbour.
22. First, place a marker at K10. Region has exactly one open cell left. Placing here clears the rest of row 10, column K, and its region.
23. Finally, place a marker at J7. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎