Preheat the oven to 180°C (350°F).
In a large mixing bowl, combine eggs and sugar.
Whisk the mixture until smooth and well combined.
Gradually add milk and vanilla extract, stirring gently.
Pour the prepared mixture into a lightly greased baking dish.
Place the baking dish inside a larger oven-safe tray filled with hot water to create a water bath.
Bake for approximately 40–50 minutes until the custard is set and the top becomes golden brown.
Remove the dish from the oven and allow it to cool at room temperature.
Refrigerate for at least 2 hours before serving.
Cut into portions and enjoy this traditional Chilean milk dessert chilled.