PREHEAT oven to 350° F. Spray two 6-cavity mini-fluted tube pans with nonstick cooking spray.
COMBINE flour, pumpkin pie spice, baking powder, salt and baking soda in medium bowl. Beat butter, brown sugar and granulated sugar in large mixer bowl for 3 to 4 minutes or until creamy. Add eggs; beat well. Add pumpkin and vanilla extract; beat well. Gradually beat in flour mixture. Spoon evenly into prepared cavities (about 1/2 cup batter in each). Gently tap pan on counter to release air bubbles.
BAKE for 20 minutes or until wooden pick inserted in cakes comes out clean. Cool in pans on wire racks for 10 minutes; invert onto wire racks to cool completely. With serrated knife, carefully cut bottoms off all cakes so surface is level/flat. (Cooks tip: save the bottoms for enjoyment later!)
BEAT cream cheese and orange extract in large mixer bowl until smooth. Gradually beat in powdered sugar. Spread 1 tablespoon mixture over cut side of 6 cakes to within 1/4-inch of edge (be sure to spread mixture over hole in center). Place the 6 cakes without icing on top of cakes with icing.
ADD 2 tablespoons milk to remaining cream cheese mixture; beat until smooth. The consistency should be thin enough to drizzle; add more milk as needed. Drizzle over cakes (use any leftover icing for the cake bottoms above). Before serving, push one cinnamon stick in center of each "pumpkin" (stick should rest on cream cheese mixture in center of cakes).