In a medium saucepan over medium-low heat, melt sugar until liquefied and golden in color. Note: If you have never melted sugar it does take some time. It first will look like hard and rocky before it starts to melt and turn into the caramel. Just keep stirring occasionally. Takes about 20 min.
Carefully pour hot syrup into a 9 inch round glass baking dish, turning the dish to evenly coat the bottom and sides. Set aside. (Tip: Have the hot water bath ready with the 9 inch pan in it. This will help to keep the baking pan warm so the caramel doesn't set up too quickly.)
In a blender add the eggs, condensed milk, evaporated milk and vanilla and blend until smooth. You can also beat these ingredients in a large bowl if you do not have a blender.
Pour egg mixture into the baking dish. Cover with aluminum foil.
Bake in a hot water bath in the preheated oven 60 minutes. Let cool completely. (Hot Water Bath: Take a large baking dish, one where the 9 inch pan will fit inside of it. Line with a wash cloth or hand towel. Pour in very hot water so it comes up half way up the 9 inch pan. Place everything in oven to bake.)
To serve, carefully invert on serving plate with edges when completely cool. (After it has cooled completely on the counter for an hour or so, I like to put it into the fridge for several hours.)