1. In a medium saucepan over medium-high heat, bring 1 cup milk and 1 cup water to a simmer. Add rice and cover; reduce heat to low and simmer until rice is tender, about 18 minutes. Uncover and increase heat to medium. Continue cooking until liquid is nearly evaporated, about 4 minutes more.

2. Meanwhile, place remaining cup milk, salt, sugar, and vanilla in a small saucepan and bring to a simmer over medium-high heat. Cook, stirring, until sugar is dissolved, about 1 minute.

3. Place egg yolks in a medium bowl. Slowly whisk in milk mixture. Reduce heat under rice mixture to low and slowly stir in egg yolk mixture; continue cooking over low heat until small bubbles start to form in the center and mixture is thickened, about 3 minutes. Remove from heat and let stand 10 minutes. Serve warm, sprinkled with cinnamon, if desired.