Preheat oven to 150 degrees C. Have ready a 23cm round baking dish.
In a blender or food processor, or using an electric mixer, combine eggs, condensed milk and vanilla and blend until smooth. In medium saucepan, cook sugar, stirring constantly, until it liquefies. When it starts to turn light brown, remove from heat and pour into waiting pan. Pour egg mixture over liquid sugar.
Line a roasting pan with a damp kitchen towel. Place baking dish on towel, inside roasting pan, and place roasting pan on oven rack. Fill roasting pan with water to reach halfway up the sides of the baking dish.
Bake 70 minutes in the preheated oven, or until knife inserted in centre comes out clean. Remove pan from water bath and let cool completely, about 1 hour. Run a knife along the edge of the pan, place a serving plate on top and invert. Serve.