Combine rice with cinnamon stick and water in a 6- to 7-quart pressure cooker pot and set over high. Cover, and lock pressure cooker lid according to manufacturer’s instructions. When steam starts to come out of the vent pipe, reduce heat to medium. Cook for 20 min. Remove from heat and let pressure drop naturally before unlocking lid. Drain any remaining liquid from pot and discard cinnamon stick.
Return pot to stovetop and set over medium. Reserve 1/2 cup coconut milk in a small bowl. add remaining coconut milk and brown sugar to rice. Cook, stirring frequently, until sugar has dissolved and mixture has thickened slightly, about 5 min. Scoop rice pudding into individual serving dishes. Drizzle reserved coconut milk over rice pudding.