Preheat your oven to 350°F (175°C). Line a muffin tray with paper liners for easy cleanup.
In a large mixing bowl, whisk together the pumpkin puree, sugar, and vegetable oil until well combined. Add the eggs one at a time, mixing well after each addition, and then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, pumpkin pie spice, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix; a few lumps are okay!
Evenly distribute the batter into the lined muffin tins, filling each about 2/3 full.
Bake for 18-20 minutes or until a toothpick inserted into the center comes out clean or with a few moist crumbs attached.
Allow cupcakes to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.