Make the cupcakes: Preheat the oven to 350°F. Prepare two cupcake pans with 14 liners (you may need end up needing more or less depending on amount of batter).
In a small bowl, stir the milk and lemon juice. Set aside for 10-15 minutes to curdle.
In a large mixing bowl or the bowl of a stand mixer fitted with a paddle attachment, whisk the flour, brown sugar, sugar, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice. Add the curdled milk mixture, pumpkin, oil, and vanilla and beat with a hand or the stand mixer until just combined.
Place about 3 tbsp (45 ml) of batter into each cupcake liner. Bake in the preheated oven for 18-22 minutes, until a toothpick inserted into the center comes out clean or with just crumbs. Allow the cupcakes to cool completely.
Frost and decorate the cupcakes: Place the frosting into a piping bag fitted with a Wilton 1M, 2D, or tip of choice. Frost a swirl on top of each cooled cupcake. Enjoy!