Combine flour, salt, baking soda, baking powder and pumpkin pie spice in a bowl.
Cream the butter, oil, and sugar until light and fluffy with an electric mixer. Add the pumpkin and eggs. Blend until combined. Scrape bowl.
Slowly add the flour mixture and mix on low until just incorporated. Do not over-mix.
Grease and flour a 10 or 12 cup bundt pan (or use baking spray with flour - Baker's Joy). Pour batter into prepared bundt pan.
Bake pumpkin bundt cake at 350˚F for 45-50 minutes or until a toothpick inserted into the thickest part of the cake comes out clean and the cake springs back when touched.
Allow cake to cool for 10 minutes before inverting onto a wire rack or serving platter. Carefully remove bundt pan and cool completely.
Use an electric hand mixer to beat the cream cheese and butter together in a large bowl. Add the powdered sugar and vanilla. Mix. Add the milk 1 Tablespoon at a time, while mixing, until the desired consistency is reached. Spread or pipe icing over the cooled cake, as desired.
Notes
Pumpkin Pie Spice is made with cinnamon, ginger, nutmeg, cloves and allspice. Use the link to make your own if you can't find it at the store.
For a thinner glaze use: 2 oz cream cheese, 2 Tbsp butter, 1/2 cup powdered sugar, 1 tsp vanilla, and 2 Tbsp milk. Drizzle over cake.
Cover well and store cake at room temperature up to 2 days or in the fridge up to 5 days. Let cake come to room temperature before eating.