Wash rice in fine sieve until water runs clear. Place in bowl; cover with 1 inch/2.5 cm water and let soak for 6 hours or overnight. Drain.

In nonstick or cast-iron skillet, sauté pan or wok over medium-high heat, boil 2 cups/500 mL of the coconut milk, stirring often, until reduced and thickened, oily and glazelike, about 10 minutes.

Meanwhile, in separate saucepan, heat remaining coconut milk to simmer; reduce heat to keep just below simmer.

Stir rice into skillet with reduced milk and reduce heat to medium-low; add salt and cook, stirring slowly and constantly in one direction only and folding over rice as it starts to absorb the reduced milk. When absorbed, add heated coconut milk, 1/4 cup/60 mL at a time, stirring and folding lightly, until completely absorbed each time.

Continue cooking and stirring, adding about 2 additions of simmering water, each 1/4 cup/60 mL, as necessary, until rice is completely tender, 15 to 20 minutes. Stir in sugar; cook, stirring, until sugar is dissolved and rice is evenly coated, about 4 minutes.

Lightly brush oil onto shiny side of each banana-leaf square. Spoon hot rice onto oiled side of one banana-leaf square; with spatula, spread into 10-inch/25 cm square. Cover with remaining banana-leaf square, oiled side down. Let cool. (Make-ahead: Cover well with plastic wrap and refrigerate for up to 3 days.)

Moistening knife with water before each slice, cut into 8 or 12 squares. Sprinkle with coconut. Serve at room temperature.

Makes 8 to 12 servings.