Peel the mangos, then cut the flesh away from the pit. Cut one of the mangos into a very small dice (you'll have about 1 1/2 cups), scoop into a bowl and sprinkle with 1 tablespoon of sugar. Gently fold to ensure that all the pieces are coated with sugar. Set aside.
Take the remaining two mangos and cut into large chunks. Transfer the chunks into a food processor and process until smooth. Scrape into a large bowl (you should have 2 cups of mango puree.) Add the sour cream and whisk until smooth, then add the rest of the ingredients and continue whisking until the sugar has dissolved. Pour the mixture into your ice cream machine and freeze according to the manufacturer’s directions.
Drain the reserved diced mango and discard the juices. Scrape the finished ice cream into a large bowl and fold in the drained mango pieces. Transfer to a resealable container and place in the freezer for several hours or overnight.
Remove the ice cream from the freezer and place in the refrigerator between 30 to 40 minutes, (depending on the depth of your container) before serving. The mango puree causes the ice cream to freeze solid. This step improves the scoopability and consistency of the ice cream.
Testing Notes: The reason you sprinkle sugar over the mango dice is to extract the extra juice from the mango.