Add whipping cream, sugar, and vanilla paste to a bowl. Beat with an electric mixer until stiff peaks form. Using a knife, make an incision at the bottom of each profiterole. Fill a piping bag fitted with a round tip with the whipped cream and generously fill each profiterole with the cream. Place the bottom side down onto the prepared serving plate.
For the chocolate ganache, add the whipping cream to a saucepan, place over high heat and bring to a boil. Roughly chop the chocolate and add it to a small bowl. Pour the boiling cream over the chocolate, and set aside for 5 minutes. Add the room temperature butter and stir well to get a smooth, creamy ganache. Drizzle the chocolate (room temp) over the profiteroles on the serving plate.