Preheat the oven to 350°F (180°C) and butter and line with parchment an 8-inch (20-cm) round cake pan. Set aside.
In a medium bowl, mix together the flour, baking powder, baking soda, pie spice, cinnamon and salt. Set aside.
In a medium bowl, whisk the pumpkin puree with the olive oil, granulated sugar, brown sugar, water and vanilla extract.
Fold the dry ingredients and the wet ingredients together until just combined, then spread evenly into the prepared pan.
Bake for 35-40 minutes, or until a skewer inserted into the center comes out clean.
Let cool completely before turning out of the pan and onto a serving plate.
Make the Cream Cheese Glaze
In a small bowl, whisk together the cream cheese and butter until smooth.
Gradually whisk in the powdered sugar followed by the vanilla extract.
Add in the milk a little at a time until your desired consistency is reached: for a thicker glaze, use less milk, and for a thinner glaze, use all of the milk.
Spread the glaze over the top and let set before serving.
Store the cake in an airtight container in the refrigerator for up to 3 days.