Beat cream cheese, butter and sugar with eletric mixer for one minute or until creamy. Add egg and vanilla and beat another minute. Add flour and beat until well blended. Place in freezer while you make cake batter, or make the day before and refrigerate overnight. (This step can be skipped, but it makes the filling easier to control it from mixing with the cake batter when baking).
To make cake batter: In a large mixing bowl, whisk together the flour, baking soda, baking powder, cinnamon, salt, cloves and ginger. In a seperate bowl, combine sugar, oil and butter until blended. Add eggs, one at a time, beating after each. Add pumpkin and water, blending well. Add flour mixture to wet ingredients and mix until combined. Pour 1/2 of batter into greased bundt pan.
Using small spoon or small cookie scoop, scoop cream cheese filling into the center of batter. Pour the rest of the batter over the cream cheese filling.
Bake for 40 min or until toothpick inserted in center comes out clean. Cool in pan for 10-15 min. Remove from pan onto serving plate and cool completely.
To make frosting: Beat cream cheese and butter with electric mixer (paddle attachment works best if using stand mixer) for one minute or until smooth. Add powdered sugar and mix until smooth and creamy. Add milk to desired consistency.
Spoon cream cheese frosting over top and allow to drizzle over sides of cake. Cover and chill in refrigerator. Store leftovers in refrigerator.