- Make a hot water bath for the flan by setting a 9-inch cake pan in a larger pan. While holding down the cake pan so it does not float, fill the larger pan with just enough hot water to come about 3/4-inch up the side of the cake pan. Then remove the cake pan and put the larger pan of water in a preheating 350°F oven while you mix the flan.
- Melt the 1/3 cup sugar directly in the cake pan the flan will be baked in. To melt evenly, hold the pan securely (wear a good oven mitt or use tongs) over or just resting on a burner; shake and tilt the pan, rather than stirring the sugar. Watch carefully. Once melted, sugar will caramelize (brown) quickly; as soon as it does, tilt pan so that bottom and the entire surface is covered. Remove from heat; syrup will harden and crack, but that's okay.
- Beat together eggs and the 7 tablespoons sugar; add milk, instant coffee dissolved in water, vanilla and cinnamon. Set caramel-lined pan in hot water in oven; pour in egg mixture carefully. Bake in a 350°F oven for about 25 minutes; test doneness by gently pushing custard in center with back of a spoon -- when done a crevice about 3/8-inch deep forms.
- Remove from hot water and chill at once. When cold, loosen custard edge with a knife, then cover with a rimmed serving plate. Holding plate in place, quickly invert. The flan will slowly slip free and the caramel sauce flow out. To serve, cut in wedges, and spoon on sauce.