Make a hot water bath, melt the 1/3 cup sugar, and coat pie pan according to directions in preceding caramel custard recipe.
Beat together eggs and the 7 tablespoons sugar.
Add milk, instant coffee dissolved in water, vanilla, and cinnamon.
Set caramelized-sugar-lined pan in hot water bath in oven; pour in egg mixture.
Bake in a 350° oven for 20 minutes or until a crevice about 3/8 inch deep forms when you gently push custard with back of a spoon at a point halfway between pan rim and center of pan.
Remove pan from hot water bath; chill.
When cold, loosen custard edge with a knife.
Cover pan with a rimmed plate and hold together; invert flan onto plate.