Bring water to a boil in a large saucepan; add rice, butter, and salt.
Place a cover on the saucepan, reduce heat to medium-low, and cook rice at a simmer until the rice is tender and the moisture is mostly absorbed, about 20 minutes.
Stir half-and-half and sugar into the rice until the sugar dissolves; add cinnamon stick and lemon peel. Bring the mixture to a boil and remove from heat.
Place a large stainless steel bowl atop a pot of simmering water.
Pour the rice mixture into the top of the double boiler and simmer, stirring occasionally, until thickened, about 45 minutes.
Pour rice pudding into a serving dish.
Remove and discard cinnamon stick and lemon peel from pudding; let cool slightly before garnishing with cinnamon to serve.
