Soak the sticky rice in water for 6 - 8 hours or overnight. Wash and rinse until the water runs clear, then let the rice drain.
Soak the mung beans in water for 3 - 4 hours, then wash and drain. Cook the mung beans in water for 15 - 18 minutes. Add butter, sugar, salt, and coconut milk to the pot and stir well until thickened. Turn off the heat and let the mung bean mixture cool down.
Cut the gấc fruit in half, scoop out the inside, remove the seeds, and squeeze the flesh tightly. Sift the chunky mass through a fine sieve to get gac juice.
In the skillet, stir-fry the sticky rice with the gấc juice, coconut milk, salt, and sugar.
Stir well until the liquid has evaporated. Turn off the heat and let the sticky rice cool down.
Cook the stir-fried sticky rice in the steamer over high heat for 20 minutes or in a rice cooker until it is well done. Open the lid and fluff the rice gently.
Fill the mold with sticky rice and use a spatula to push it down tightly until compact and as thick as one-third of the mold. Remove the mold and transfer the layer of sticky rice to a plate.
Repeat the layering process, but after the rice, add a compact layer of mung beans, one-third the mold's depth. Top with the rice again, pressing lightly to ensure all layers adhere.
Get Xôi Gấc Đậu Xanh out of the mold, plate it, and garnish with toasted sesame seeds and coconut flakes.