Preheat the oven to 160°C (320°F). Line a 12-cup cupcake pan with cupcake liners.
In a large bowl, whisk together flour, baking powder, baking soda, salt, pumpkin spice, and brown sugar.
In a separate bowl, whisk together pumpkin purée, oil, eggs, and vanilla extract until smooth.
Pour the wet mixture into the dry and gently stir with a spatula until combined. Do not overmix.
Divide the batter evenly into the cupcake liners and bake for 23 to 24 minutes. Let cool 5 minutes in the tin, then transfer to a wire rack.
To make the frosting, beat butter and brown sugar in a stand mixer for 5 minutes until fluffy. Add cream cheese and vanilla and beat again.
Gradually add powdered sugar in two parts and mix until the frosting is smooth and creamy.
Once cupcakes are fully cooled, pipe the frosting on top using a piping bag. Decorate as desired.