Preheat oven to 350°F. Grease an 8 inch round cake pan with cooking spray and place a sheet of parchment paper in the bottom of the pan.
Whisk together the flour, cocoa powder, salt, baking soda, baking powder, and pumpkin pie spice in a medium bowl and set aside.
In a large bowl of a standing or handheld mixer, beat together vegan butter and sugars. Add in the pumpkin puree and mix again.
Add in eggs and beat for another 30 seconds or so, scraping the sides of the bowl with a spatula. Pour in the milk and continue mixing.
Slowly add the dry ingredients into the bowl of the standing mixer and mix until combined.
Pour the cake batter into the prepared pan and bake for between 45-55 minutes, or until a toothpick inserted in the middle of the cake comes out clean, or almost clean. There shouldn't be any wet batter on the toothpick but its okay if the cake leaves a bit of colour on it.
Leave the cake in the pan until cooled completely.