Preheat the oven to 350F degrees. Generously grease a 12-cup capacity bundt pan.
In a large bowl, whisk together the gluten-free flour, pumpkin pie spice, baking soda, baking powder, and salt.
In the bowl of a stand mixer, beat together the shortening, granulated sugar and brown sugar on medium speed for 1-2 minutes until creamed. Add the oil, vanilla and eggs and mix until smooth, scraping down the sides and bottom of the bowl halfway through.
With the mixer running on low, add ⅓ of the dry ingredients and mix until combined. Add ½ the pumpkin and continue to mix. Repeat, alternating with the remaining flour and pumpkin.
Pour the batter into the prepared bundt pan and smooth the top.
Bake for 60-70 minutes, or until an inserted toothpick comes out clean and the top feels slightly firm to the touch.
Cool the cake in the pan for 20-30 minutes. Then carefully insert the pan, to let the cake slide out and continue cooling on a wire rack.
Let the cake cool completely before frosting. To make the frosting, in a medium bowl beat together the butter and cream cheese until light and fluffy.
Beat in the powdered sugar followed by the milk and vanilla.
Beat in a little extra powdered sugar or milk if needed, until the glaze is thin enough to drizzle.
Place the cake on a serving platter and drizzle with the glaze.
Slice and enjoy!