Preheat and prep: Get your oven to 160°C (320°F). Line the muffin tin with paper liners.
Whisk the dry stuff: In a large bowl, whisk together the flour, dark brown sugar, baking powder, baking soda, pumpkin pie spice, and salt. Make sure there are no lumps of brown sugar — break them up with your fingers if needed.
Mix the wet stuff: In a separate bowl, whisk together the pumpkin puree, vegetable oil, eggs, and vanilla until completely smooth.
Combine gently: Pour the wet ingredients into the dry ingredients. Stir with a spatula or whisk until just combined — about 15 strokes. A few small streaks of flour are okay.
Fill and bake: Divide the batter evenly among the 12 liners — about 1/4 cup per liner. Bake for 23–24 minutes, rotating the pan halfway through. The cupcakes are done when a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool the right way: Let the cupcakes rest in the pan for exactly 5 minutes, then move them to a wire rack to cool completely.
Make the frosting: About 10 minutes before you start, take the butter and cream cheese out of the fridge. In a stand mixer with the paddle attachment, beat the butter and brown sugar on high speed for 5 minutes. Scrape, then mix for 2 more minutes. Add the vanilla and cream cheese, then beat for 1 minute on medium speed. Reduce speed to low and gradually add the sifted powdered sugar in two additions. Once all the sugar is in, beat on medium for 2 minutes. If too soft, chill for 10 minutes.
Pipe and finish: Transfer the frosting to a piping bag fitted with a large round tip. Pipe onto the cooled cupcakes in a swirl starting from the outside edge and working inward. Optionally dust with pumpkin pie spice or cinnamon.