Charlie, while I have never made pesto with cream, the first thing that jumped out at me was, 1 cup of oil (to one cup of basil), i.e. sounds like a lot of oil (i.e. the ratio of basil to oil). Usually, I see about 1/4 cup oil & about 1-2 cups basil (herbs), but that is not to say the recipe will not be good or turn out well. Seems like a lot of oil to be added to the cream as well (i.e. 1 cup cream & 1 cup oil). These recipes do not include cream, but maybe there's one here you might like to try, as well.
Edited to add: I found a recipe using heavy cream, that looks good:
Alfredo Pesto Pasta