S46 TRACON Controller reported an aircraft descended below their assigned altitude and flew below the minimum vectoring altitude.

Narrative

Aircraft X was on a heading of 110 to avoid weather over a mountain range. I issued a descent to 11000 ft. from 12000 ft. (11000 ft. is the MVA in that area) with a good readback from the Pilot. I observed the aircraft at 10700 ft. and restated to maintain 11000 ft. The Pilot responded that they were on their way back up and they thought the clearance was to 10000 ft. I then issued a low altitude alert to which they responded they were on their way back up. I observed them a get to 10500 ft. before climbing back up. Luckily when this happened; they were east of the ridgeline and headed for lower terrain. Suggestion: This was Pilot error that I think I caught just about as soon as I could. With him reading back the altitude correctly there is not much more I could have done differently in this situation to fix it. I did not issue a brasher warning at the time because they were entering a critical phase of flight to final; but I should have had tower issue a Brasher warning once they were on the ground to ensure the Pilot was aware of their mistake and at least prevent this from happening to this particular Pilot again.