Preheat oven to 350 degrees. Line your cupcake pan with paper liners.
In another bowl, blend the pumpkin, sugar (both white and brown), and the vegetable oil until thoroughly mixed.
Add the eggs, one at a time, beating after each addition.
Add flour mixture, one half at a time, and mixing well after each addition.
Spoon the batter into the lined baking cups, filling each about two-thirds full.
Remove from the oven. Allow the cupcakes to cool in the cupcake pan for 10 minutes, then transfer to a wire rack to cool completely.
Slowly pour in the milk, continuing to stir until it comes to a boil. Set aside to cool, then transfer to a mixing bowl.
Add spoonfuls of powdered sugar to the mixture a little at a time, mixing after each addition. If the frosting is too thin, add an additional tablespoon of powdered sugar at a time until it thickens.