Heavy cream = whipping cream in the little pint cartons. If you put it in a bowl and whisk it vigorously with a little sugar and maybe a touch of spiced rum you'll have a delicious whipped cream.

But traditional/real carbonara has no cream in it, so I'm not sure what the recipe writers were thinking. In real carbonara the sauce is egg, parmesan, and a little of the rendered fat from frying guanciale/pancetta/bacon.