Pumpkin Cupcakes: Preheat the oven to 350 degrees F. Line a 12-count muffin pan with cupcake liners and set aside.
In a large bowl, stir together the flour, baking powder, baking soda, salt, and pumpkin pie spice until combined and set aside. In a medium bowl, whisk the brown sugar, granulated sugar and eggs together until combined. Add the pumpkin, oil, milk, and vanilla and whisk until combined. Pour the dry ingredients into the wet ingredients and gently stir until just combined, being careful not to over mix.
Spoon the batter into the prepared cupcake cups, filling them about 1/2 of the way full. Bake for 17-19 minutes or until a toothpick inserted in the center comes out clean. Transfer cupcakes to a cooling rack and allow to cool completely before frosting.
Cream Cheese Frosting: In a large bowl with an electric mixer, beat together the butter and cream cheese until smooth, about 1 minutes. Add the vanilla and powdered sugar and beat on medium speed until smooth and combined, about 3 minutes. Transfer frosting to a piping bag and pipe frosting on to cooled cupcakes.
Brown Butter Maple Drizzle: In a medium saucepan over medium-high heat, melt the butter. Allow to cook until brown specs begin to form at the bottom of the pan, about 3 minutes. Once formed, stir immediately and remove from heat. Add the powdered sugar, vanilla, maple syrup and water and stir vigorously until smooth. Add more water a tablespoon at a time until you get the desired consistency. Drizzle over frosted cupcakes.