Wash the grapes and cut a very thin slice of skin off of the bottom of each grape so that they will sit upright. Cut the tops off and discard. Scoop out some of the flesh with a sharp paring knife to create a small cavity in each grape.
In a small bowl, mash the goat cheese with enough cream to make a smooth, icing-textured mixture. Spoon into a small piping bag, or resealable bag with the corner tip cut off. Pipe some of the goat cheese mixture into each grape and then sprinkle the tops with some chopped pistachios.