Preheat oven to 350 degrees Fahrenheit. Heat up 6 cups of water for the water bath. Put the plate into a baking pan that is larger than the pie plate.
Heat up sugar in a small saucepan. In about 3 minutes, it will start to turn into crystals. Keep stirring until it becomes a smooth caramel. Pour into a pie plate.
In your stand mixer, mix the eggs for 30 seconds. Add vanilla extract, sweetened condensed milk, salt and water. Mix until mixture comes together.
Pour the mixture onto the pie plate. Slowly pour the hot water into the baking pan up to 1 inch of the baking pan. Be careful not to splatter into the pie plate. Slowly, put the baking pan into the oven.
Bake for 55-60 minutes. Check if the middle of the pie plate does not jiggle. Slowly take out of the oven. Take out the pie plate out the baking pan. Cool completely and put in the refrigerator for 3 hours or overnight.
When you are ready to serve, put a knife around the edge of the pie plate to loosen the flan. Invert into a large plate and serve.