In a bowl soak rice in cold water to cover 30 minutes and drain in a sieve. Rinse rice under cold water and drain.
In a small saucepan blanch pistachios in boiling water 3 minutes and drain in a sieve. Rinse pistachios under cold water and pat dry. Rub off pistachio skins and chop pistachios coarse.
In a heavy 1-quart saucepan melt butter over low heat and cook cardamom, cinnamon, nutmeg, and sugar, stirring, 1 minute. Add rice, milk, and cream and simmer gently, uncovered, stirring occasionally, until rice is tender, about 18 to 20 minutes.
Cool pudding and transfer to a serving dish. Stir in pistachios and bananas. Chill pudding, covered, at least until cold, about 4 hours, and up to 2 days.
Garnish pudding with pistachios and serve with compote.
