In a skillet, heat 1 tablespoon oil over medium-low heat. Add mango and sweat mango until soft.
Stir in sugar and let cool.
Put mango in a blender and puree.
Add egg yolks and lime juice. While blender is running, slowly drizzle in remaining 3/4 cup oil. If necessary, add a splash of cold water to loosen up the aioli.
Season to taste with salt and pepper. Spoon into a serving bowl.
Note 1: If the mango is very ripe, you may not want to add sugar. If it’s not too ripe, you may want to add more sugar.
Note 2: This recipe uses raw eggs which can be a health hazard, especially for children, the elderly, or pregnant women.