Soak the sticky rice overnight in water to cover; drain.
Line a bamboo steamer with dampened cheesecloth. Spread the rice on the cheesecloth in an even layer. Set the steamer in a wok over boiling water. Cover and steam the rice until tender, about 15 minutes; transfer to a bowl.
Meanwhile, in a small saucepan, simmer 1 1/4 cups of the coconut milk with 1/4 cup of sugar, stirring to dissolve the sugar. Stir the coconut milk into the rice and season with salt; keep warm.
In a small saucepan, simmer the remaining 1 cup of coconut milk over moderately high heat until reduced by half, about 15 minutes.
In a medium skillet, cook the remaining 2 tablespoons of sugar with the oil over moderate heat until caramelized, about 2 minutes. Add the puffed rice and stir until coated, then transfer to a plate to cool. Spread a piece of banana leaf on each plate. Mound the sticky rice on the leaves, pour some of the reduced coconut milk over the top and garnish with the caramelized puffed rice. Pile the mango sticks next to the rice and serve.
A fruity-floral dessert wine, such as a Muscat de Beaumes-de-Venise, will complement the sweet, tropical flavors of the dish.