Whisk eggs, condensed milk, evaporated milk, milk, and vanilla extract in a large bowl. Set aside.
Caramelize sugar in the cooking container over medium-low heat until amber, then coat the sides carefully.
Cool the caramel-coated pot for at least an hour.
Preheat the oven to 350°F. Heat water for the bath.
Strain the custard mix into the pot, avoiding air bubbles.
Cover the pot, place it in the larger pot, add water to 75% height, and bake for 1 hour 15 minutes or until set.
Cool for 30 minutes to an hour, then refrigerate for at least 10 hours or overnight.
To unmold, tap the container, cover it with a plate, and flip.
Let the flan naturally release from the container and serve.