Place the 1/2 cup rice in a colander and rinse well with cold water.
Combine rice, 2 cups water, and the 2 cinnamon sticks in a large pot and bring to a boil over medium-high heat. Reduce heat to medium low and simmer, uncovered, until rice is cooked, stirring ocassionally to prevent sticking, about 10 minutes. Discard one of the cinnamon sticks and let cool slightly.
Transfer rice mixture with the other cinnamon stick to a blender. Add the 2 3/4 cups whole milk, 1 1/4 cups half and half, 1/2 cup sugar, and pinch of salt and blend on high until smooth. Return mixture to the pot.
Bring to a simmer over medium-low heat. Don't let it boil. Let simmer until slightly thickened, and serve hot with extra ground cinnamon on top and a cinnamon stick if desired.
