Measure the heavy cream into a liquid measuring cup. Put 1/2 cup water in a small, heavy saucepan with steep (at least 4-inch) sides. Add the sugar and swirl the pan to moisten it. Cover and bring to a boil over medium heat, swirling the pan occasionally, until the sugar dissolves, about 1 minute. Increase the heat to high and cook, still covered but checking frequently, until the sugar starts to turn light brown, 3 to 7 minutes. Remove the lid and continue to cook, swirling the pan occasionally, until the sugar turns dark amber, 2 to 4 minutes. Immediately remove the pan from the heat, and slowly and very carefully stir in the heavy cream; it will bubble and splatter. Continue to stir until the sauce is smooth.

Pour the caramel into a small, heatproof bowl, and let it cool slightly. Stir in the espresso and the Kahlua, if using.

To serve: If the caramel is cold or has thickened from sitting, reheat it gently over low heat. Put a scoop or two of ice cream into six individual cups or dishes. Drizzle some caramel on top and sprinkle with a spoonful of espresso beans, if using.