Place potatoes in a large saucepan and cover with water.
Add salt and stir to dissolve.
Bring to a boil over high heat.
Reduce to a low boil and cook, stirring occasionally, until liquid has completely evaporated and potatoes are covered in a film of salt, about 45 minutes.
Remove from heat and let potatoes rest for 5 minutes in pan.
Toss again, then transfer to a serving bowl.
Serve with ají.
