Puree mango, sugar, lime juice and salt in a food processor, scraping down sides of work bowl occasionally.
Add yolks then puree 15 seconds longer.
Strain through strainer set over large metal bowl, pressing on solids with back of spatula to release as much puree as possible.
Discard solids in strainer.
Set metal bowl over saucepan of simmering water (do not allow bottom of bowl to touch water).
Whisk puree until thickened and thermometer registers 170°F., about 10 minutes.
Remove from over water.
Whisk in butter 1 piece at a time.
Cover and refrigerate overnight.