To prepare pudding, combine first 4 ingredients in a large, heavy saucepan; bring to a boil. Reduce heat, and simmer, uncovered, 20 minutes or until rice is tender. Drain.
Return rice and cinnamon stick to pan; stir in milk, 1/2 cup sugar, and ground cinnamon. Bring to a simmer over medium heat, stirring constantly. Reduce heat to medium-low; cook 30 minutes or until thick, stirring frequently. Discard cinnamon stick. Remove from heat; stir in 1 teaspoon vanilla and 1/2 teaspoon almond extract.
To prepare sauce, combine cherries and 1 1/2 cups water in a medium saucepan; bring to a boil. Reduce heat, and simmer 20 minutes. Stir in 2 tablespoons sugar; cook 5 minutes. Combine 1 tablespoon water and cornstarch. Add to cherry mixture; bring to a boil. Cook 1 minute or until slightly thick, stirring constantly. Remove from heat; stir in 1/2 teaspoon vanilla and 1/4 teaspoon almond extract. Serve pudding with sauce.