Place 1 cup sugar in heavy saucepan and carmelize* over medium heat. Pour into a 2 quart high-sided metal mold, such as an aluminum flan mold or charlotte mold. Tip the pan so the caramel coats the bottom and sides, working fast as the caramel hardens quickly.
Whisk together egg yolks, whole eggs, evaporated milk, 3/4 cup sugar and vanilla. Pour into caramelized mold. Cover tightly with foil. Place in a larger pan and pour in about 1-1/2 inches of hot water around the sides.
Place on the bottom rack of oven and bake approximately 55 minutes. Test doneness by inserting a knife into the middle. If large curds cling to the knife, cook for 10 minutes longer. If just a film clings, the flan is done. It should shimmer in the middle but look cooked around the edges.
Remove from oven and cool to room temperature. Refrigerate at least 2 hours before serving.
*to carmelize sugar, swirl sugar in heavy saucepan over medium heat -- do not stir as this will cause clumping -- until sugar begins to liquify. After the sugar liquifies, stir with a wooden spoon. When it turns light brown, it's caramelized.