Pick ripe mangoes. Press the mango. If it feels soft, it is ripe. If the mangoes are hard, leave them on the counter for a couple of days until they turn from green to red.
Boil the water. Bring 4 cups of water to a full rolling boil. Do not add the pearls to cold or lukewarm water, because the starch dissolves into a paste.
Cook the tapioca. Add the pearls to the boiling water and set a timer for 20 minutes. Stir once at the start so they do not stick.
Prepare the mangoes. While the pearls cook, peel the mangoes and cut the flesh away from the pit. Cut the flesh into chunks and trim off any fruit left on the pit. Set aside the best chunks of one mango for topping.
Check the pearls. After 20 minutes, look for white dots in the center. If you still see white, turn off the heat and let the pearls sit in the hot water for 2 to 5 minutes. They are done when they are clear all the way through.
Cool the pearls. Drain the pearls and transfer them to a large bowl of cold water. Swap out the warm water for fresh cold water until the pearls are completely cool. Do not use ice, because it hardens the pearls.
Blend the mango cream. Add the remaining mango, coconut milk, condensed milk, and vanilla to the blender. Blend until smooth, then scrape it into a large bowl with a rubber spatula.
Combine. Drain the pearls well. A little water is fine, but not too much. Stir them into the mango mixture.
Serve. Scoop into bowls and top with the reserved mango chunks.