Preheat oven to 350°F (175°C). Make the caramel by cooking sugar and water until deep amber, then pour into a 9-inch round pan.

Blend eggs, sweetened condensed milk, evaporated milk, vanilla, and salt until smooth. Pour over the caramel.

Place the pan in a water bath with hot water reaching halfway up the sides. Bake 50 to 60 minutes until set at the edges and jiggly in the center.

Cool, then chill at least 4 hours. Run a knife around the edge, invert onto a plate, and serve with the caramel sauce.