Mix the oatmeal, flour, cinnamon, ginger, baking powder, salt and nutmeg in a mixing bowl. Set aside.
Beat together sugars and butter for about a minute. Add in pumpkin and vanilla and beat well. Fold in dry mixture. Cover and refrigerate for 30 minutes.
Preheat oven to 375 and line 2 baking sheets with parchment paper. Use a 2 tablespoon portion scoop to scoop dough onto a baking sheet, about 2" apart. Gently press down each cookie until it's about ½" thick. Bake for 11 minutes or until bottoms just begin to brown. Cool completely before icing.
To ice cookies, add powdered sugar and milk in a small bowl and mix well. Use a spoon to drizzle onto the cookies. Let stand to harden and serve.
Makes 24 cookies.