Combine the rice and water in a saucepan; bring to a boil; cover and reduce heat to low. Simmer until water is absorbed, 15 to 20 minutes.
While the rice cooks, mix together 1 ½ cups of coconut milk, 1/4 cup sugar, ½ teaspoon of salt in a saucepan over medium heat; bring to a boil; remove from heat and set aside. Stir the cooked rice into the coconut milk mixture; cover. Allow to cool for 1 hour.
Make sauce by mixing together ½ cup coconut milk, 1 tablespoon sugar, ¼ teaspoon salt, and the tapioca starch in a saucepan; bring to a boil, then remove from heat.
Serve sticky rice with mangos and pour sauce on top. Sprinkle with sesame seeds.