There are many ways to make rice pudding: on the stove, baked in the oven or a combination of the two. You can make the custard separate from the rice and combine them after and it can be so many different kinds of custards. The nice thing about a baked one is you can make it the night before to enjoy for a special breakfast the next day. Serve it with a dollop of whipped cream and a sprinkle of cinnamon if you like.
In a covered heavy saucepan, bring the rice, milk, apricots, vanilla scrapings, and lemon zest to a simmer over medium heat. Immediately reduce the heat to as low as possible, cover tightly, and simmer gently, stirring occasionally, until the rice is very tender, 20 to 25 minutes. Turn off the heat.
Stir the sugar into the cooked rice mixture. Stir in the egg yolks. Pour the rice pudding into a greased baking dish and bake for 20 minutes until slightly browned on the top. Remove from the oven and let cool. Chill until ready to serve.