Add rice and 1 cup water in a medium sauce pan and let rice soak for 1 hour.
Add another half cup water to the rice and half the coconut milk, salt, and white sugar. Stir to combine. Bring to a gentle boil over medium-high heat. Reduce heat to medium-low to get a gentle simmer, partially cover and simmer until all the liquid has been absorbed by the rice, 20 to 30 minutes. Turn off heat and leave the saucepan tightly covered on the burner for another 10 minutes.
While rice is cooking, prepare mangoes by peeling them and cutting in half longways to remove the seed. With opened side-down on a cutting board, cut each half into 5 crosswise slices. Place cut halves on a plate and refrigerate until ready to use.
Make the sauce in a small saucepan by warming the remaining coconut milk over medium-low heat, about 5 minutes. Add brown sugar, stirring until it dissolves.
To serve, fluff rice and scoop out ¼ of the rice to a bowl or plate. Pour ¼ of the sauce over and around the rice. Add a half mango slices next to the rice. Sprinkle lightly with sesame seeds and serve