Combine all ingredients for the base in a food processor and blend for 2-3 minutes, until almost smooth.
Spoon the mixture into paper cups. Use your fingers to press the mixture to the bottom and the sides of the cups (it is easier if you put them on a muffin tin). Keep the cups in the freezer until preparing the filling.
Combine the dates, vanilla and coconut oil in a food processor. Add also some of the water (start with little and then keep adding if needed). Blend for few minutes until smooth. The consistency of the filling should be like a puree.