Combine Cocoa PEBBLES™ cereal and milk in a cereal bowl. Allow to sit for 30 minutes. Strain out milk and discard cereal. Set aside.
Add water and cocoa powder to a heavy saucepan over medium-high heat. Bring water to boil. Stir in rice and salt. Return water to boil. Reduce heat to low. Cook, covered, until water is absorbed, and rice is tender, about 15 minutes.
Stir in cereal milk and cinnamon sticks. Increase heat to medium-high; bring milk to boil. Reduce heat to low. Cook, uncovered, stirring occasionally to prevent sticking and scorching, until mixture is thick and creamy, about 25 minutes. Remove cinnamon sticks. Stir in condensed milk, chocolate and vanilla. Cook, stirring often, until chocolate is melted and combined, about 2-3 minutes more. Cool completely.
Pour rice pudding into serving bowls, chill at least one hour. Sprinkle with cinnamon and additional Cocoa PEBBLES™ cereal before serving.