In a large, heavy saucepan, stir in rice, whole milk, coconut milk, salt, cinnamon, and nutmeg. Bring to a boil over high heat, stirring constantly. NOTE: If you would like your rice pudding to be white, reduce the amount of both cinnamon and nutmeg to a pinch and add them at the very end of the cooking process along with the lemon zest.
Reduce the heat to medium-low, cover, and simmer gently, stirring occasionally, for approximately 20-25 minutes. Then, uncover, add the condensed milk, and continue cooking (uncovered) over medium-low, stirring frequently, for about 8-10 minutes or until the rice is tender and the pudding is reduced a bit. Remove pan from the heat.
In a medium bowl, whisk the egg yolks, sugar, and vanilla extract together. Slowly add this mixture to the cooked rice, whisking constantly. Set the pan over medium-low heat and cook, stirring and scraping the sides and bottom of the pan constantly with a wooden spoon, for about 1 minute. Remove the pan from the heat, stir in grated lemon zest, and transfer rice pudding to serving bowls/dishes. Serve warm, at room temperature, or chilled. Right before serving, rice pudding can be garnished with a sprinkle of cinnamon and lemon zest.
NOTE: If ungarnished rice pudding is not served immediately, place a sheet of plastic wrap right on the pudding's surface to prevent a skin from forming.