Set oven to 350 degrees F (set oven rack to second-lowest position).
Prepare (2 )9 inch cake pans fitted with paper liners fitted in each pan.
For the cupcakes; In a large mixing bowl beat together the oil with eggs, sugar, pumpkin puree and vanilla until well combined.
In another bowl combine the flour with the next 4 ingredients; add to the pumpkin mixture and beat until well combined.
Fill each tin about three-quarters full.
Bake for about 18-22 minutes or until cake test done.
Cool completely before filling.
For the frosting; in a bowl beat the cream cheese with butter, vanilla and cream until fluffy.
Add in confectioners sugar and beat until creamy (adding in more cream or milk if necessary to achieve the right consistency for spreading).
Spread onto the top of cake after cake is cool.