Melt the butter in a saucepan.
Add the sugars, rum, brandy, corn, syrup, and cream.
Cook at low to medium heat, stirring occasionally with a wooden spoon until the sugars dissolve and the sauce simmers and thickens. The mixture will double in volume.
Take the sauce off the heat. Cool for about 5 minutes.
In a small dish, bowl or dish beat the egg yolks. Take a small about of the Brandy-Rum Caramel Sauce and whisk it into the egg mixture. Repeat the process several times until the egg yolks have been incorporated into the caramel sauce. This will temper the eggs.
Return the egg mixture into the sauce and stir with a wooden spoon. Return to heat low-medium heat. The mixture will thicken and double again.
Remove from heat. Let the mixture cool down for about 5 minutes. Pour thorough a sieve to make sure that the mixture is smooth.
Serve warm over bread pudding, cheesecake, or ice cream.
Note: Make sure that your saucepan is tall because the mixture will double in volume as it cooks.