Heat oil in a deep pot or deep skillet to 375 degrees F (190 degrees C).
Combine flour, baking soda, cinnamon, pumpkin pie spice, baking powder, and salt in a bowl.
Beat milk, pumpkin purée, egg, and brown sugar together in a large bowl with an electric mixer until well blended. Stir in flour mixture until smooth.
Put your finger over bottom opening of a funnel; fill funnel with ½ cup batter. Holding funnel close to surface of oil, release batter into oil while making a circular motion. Fry until golden brown. Use tongs and a wide spatula to carefully turn funnel cake. Fry until golden, about 1 minute more. Drain on paper towels. Repeat with remaining batter. Cool for 5 minutes. Dust generously with confectioners' sugar.
