Rinse the rice under cold water until water runs clear. In a large saucepan, combine rice with 2 cups of water and bring to a boil over medium-high heat. Reduce heat to low and simmer for 10 minutes until rice is partially cooked and water is absorbed.

Add the milk to the rice and stir well. Increase heat to medium and bring to a gentle simmer. Cook for 35-40 minutes, stirring frequently to prevent sticking, until rice is very tender and mixture has thickened considerably. The rice grains should be soft and suspended in creamy liquid.

While rice cooks, preheat your oven to 400°F (200°C). In a mixing bowl, whisk together eggs, sugar, vanilla extract, and a pinch of salt until well combined and slightly frothy.

Remove rice mixture from heat and let cool for 5 minutes. Slowly add a ladleful of the hot rice mixture to the egg mixture while whisking constantly to temper the eggs. Repeat with another ladleful, then pour the tempered egg mixture back into the saucepan with the remaining rice, stirring constantly.

Return the saucepan to low heat and cook for 3-4 minutes, stirring continuously, until the mixture thickens slightly. Do not let it boil or the eggs will scramble.

Divide the rice pudding mixture evenly among 8 ramekins or a large baking dish. Place the ramekins on a baking sheet. Bake in the preheated oven for 15-20 minutes until the tops are golden brown with caramelized spots.

Remove from oven and let cool to room temperature. Dust with ground cinnamon if desired. Refrigerate for at least 3 hours or overnight until thoroughly chilled before serving.