Preheat the oven to 350°F, 177°C or gas mark 4. Line 2 muffin pans with paper cupcake liners.
In a mixing bowl combine the flour, baking powder, salt, and pumpkin spice. Whisk or sift together and set aside.
In the bowl of a stand mixer add the oil and butter and beat on a medium speed. Add the sugar and increase the speed until light and fluffy.
Add the eggs one of the time waiting a minute between each egg. Add the vanilla extract and reduce the speed to low. Add the flour mixture and mix until just incorporated. Add the pumpkin and mix until just incorporated.
Using a cookie scoop at 4 tablespoons or ¼ cup of batter to each cupcake well.
Bake for 20 minutes, rotating the cupcake pans halfway, or until a toothpick inserted into the center comes out clean. Allow to cool in the pan for at least 10 minutes before placing them on a cooling rack. If you are using only one pan allow the pan to cool for another 5-10 minutes before lining and filling the cups to bake.
Making the Cream Cheese Frosting:
In the bowl of a stand mixer fitted with the paddle attachment beat butter, cream cheese, and maple syrup on medium speed until smooth and creamy. Scrape the bowl a few times.
Add the pumpkin spice and powdered sugar. Blend on low until all of the sugar is incorporated. Once all of the sugar is mixed in increase the speed to high and beat for 30 seconds until light and fluffy. Place into a piping bag with a star tip and pipe over the cooled cupcakes.