Add the rice, water, lemon peel, cinnamon stick, and pinch of salt to a large saucepan. (I like to use a non-stick, heavy-bottomed pot)
Cook over medium heat while stirring frequently for 20 minutes. The water should be absorbed and the rice should be softened.
Remove the pot from the heat and stir in the condensed milk, whole milk, and vanilla. Place back on the stove and lower to medium low.
Cook for 30 minutes while continuously stirring. If the bottom starts to stick, lower your heat and do NOT scrape the bottom of the pot. This will only loosen burnt bits and incorporate them into your rice and we don't want that.
The mixture will be thickened after the 30 minutes but will continue to thicken as it cools.
Add the rice pudding to a bowl or individual dishes, top with a bit of ground cinnamon, and refrigerate for a few hours until cooled.