Preheat oven to 350F/180C. Line a 12 cup muffin tin with liners.
Using a handheld mixer or stand mixer fitted with a paddle attachment, beat the butter, oil and both sugars together on medium-high speed until creamed, about 2 minutes. Scrape down the sides and bottom of the bowl as needed. Add the eggs, pumpkin puree and vanilla extract. Then beat on medium-high speed until combined, about 1-2 minutes. Scrape down the sides and bottom of the bowl as needed. Set aside.
Mix the flour, baking soda, baking powder ,pumpkin pie spice and salt in a small bowl and set aside.
Add the dry ingredients into the wet ingredients and mix on medium speed until well combined..
Spoon batter evenly into the prepared pan, filling them about ⅔ full. Bake for about 20-22 minutes.
Once baked, take them out of the cupcake pan and place them on a wire rack to cool completely.
Once cooled, frost the cupcakes with the prepared frosting and drizzle salted caramel sauce on top.