Combine coconut cream, coconut milk, and whipping cream in a medium saucepot. Bring to a simmer over medium heat. Slowly temper the sugar-egg mixture by pouring in the hot milk mixture in a steady stream while whisking constantly. (This ensures that you don't end up with scrambled eggs.) Pour mixture back into saucepot and bring to a boil for 1 minute, whisking constantly. Remove from heat. Add butter and vanilla extract.