Preheat the oven to 350 degrees F. Line your muffin tins with 24-30 paper liners, depending on the size. (Some "standard" sized muffin tins are larger than others.)
In a bowl of your electric mixer, combine the flour, sugars, spices, baking powder and soda, and salt. Mix well. Then turn the mixer on low and slowly add the melted butter, eggs and pumpkin puree. Scrape the bowl and beat again until the batter is totally smooth.
Using a 1/3-cup scoop, fill the paper liners about 2/3 full. Then bake for 18-22 minutes, until a toothpick inserted into the middle of a cupcake comes out clean. Cool in the muffin tins for at least 10 minutes.
Flip the pumpkin cupcakes out of the muffin tins, and allow them to cool to room temperature before making the frosting.
For the Peanut Butter Frosting:
Place the softened butter in a clean mixing bowl and beat until light and fluffy. Add the peanut butter and beat again. Scrape the bowl, then beat on low while adding the powdered sugar, milk, vanilla and salt. If the frosting is too thin, add a little more powdered sugar. If it is too thick, add another tablespoon of milk.
Scoop the frosting into a large piping bag with a large tip and pipe the frosting onto the cooled pumpkin cupcakes. To garnish, sprinkle with pumpkin pie spice, chocolate sprinkles, or top with a pumpkin candy.