Strain egg mixture into another large bowl. Pour custard into another large bowl. Pour custard into prepared ramekins, dividing equally. Pour enough hot water into baking pan to come halfway up sides of ramekins. 4 Bake flans until center is gently set, about 35 minutes.
Transfer flans to rack and cool.
Cover and chill overnight. Turn over onto plate. Lift off ramekin, allowing syrup to run over flan. Repeat with remaining flans. Increase heat and boil without stirring until syrup turns deep amber color, occasionally brushing down sides of pan with wet pastry brush and swirling pan, about 10 minutes.