Put the coconut milk, milk, rice, salt and sugar in a small saucepan and bring to a boil over medium-high heat. Reduce the heat so the liquid simmers very gently. Cook uncovered, stirring occasionally, until rice is tender but chewy and absorbs most of the liquid, about 1 1/2 hours.
Remove the pudding from the heat and transfer to a bowl, or divide among 4 to 6 individual bowls. Press plastic wrap directly on the surface of the pudding and cool in the refrigerator, about 1 hour.
To serve, top with brown sugar, banana, and a scoop of ice cream.
Other topping suggestions: Diced fresh pineapple with toasted coconut and finely grated lime zest, berries or peaches sweetened with honey or 2/3 cup dried blueberries steeped in 1/2 cup boiling water.
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