Preheat oven to 250°F.
In a large frying pan, place 1 cup sugar and cinnamon.
Place pan over low heat and caramelize, stirring continuously, until amber colored.
Remove from heat. Slowly add water while stirring.
Immediately pour caramelized sugar into four 8-ounce ramekins, swirling the cups to evenly coat the bottom.
Pour milk in a saucepan.
Place saucepan over medium-low heat. Cook until almost simmering. Remove from heat and set aside.
In a medium mixing bowl, add eggs, egg yolks, remaining 3/4 cup sugar and vanilla. Beat with a whisk until pale yellow in color.
Gradually add hot milk to egg mixture while stirring continuously.
Strain milk/egg mixture through a fine-mesh strainer.
Pour mixture into the ramekins, dividing equally. Skim any foam or bubbles off the surface of the custard.
Place the ramekins in a roasting pan.
Fill the pan with 2 inches of warm water, so that the water comes about halfway up the outsides of the ramekins. Do not get water into the ramekins.
Cover ramekins with a sheet of parchment paper.
Place pan of custards in preheated oven. Bake 1 1/2 to 2 hours, or until a toothpick comes out clean when inserted in the middle of the flans.
Remove from oven. Cool to room temperature on a cooling rack.
Cover with plastic wrap and place in the refrigerator overnight.
Remove ramekins from water.
Run a knife around the inside edge of the ramekins to loosen the flans.
Gently invert and turn out the flans onto serving plates.
Serve cold.