In a medium-size saucepan, melt the butter over medium heat. Add 1 cup of the cream and and whisk until blended. Add the additonal 1 cup of cream to achieve the amount of Sea Food flavor you are looking for. Simmer the sauce, whisking, until reduced by about ¼.
Remove the pan from the heat, add the basil pesto, lemon juice and Parmesan cheese and whisk until the cheese is melted and the sauce is thoroughly blended. Season to taste with salt and pepper.