In a large bowl, cream butter, shortening and sugars until light and fluffy.
Beat in molasses and vanilla. Add the flour, baking soda, and salt, nutmeg, and cinnamon. Mix well. Fold in oats.
Drop dough onto greased (or parchment paper-lined) baking sheets using a medium cookie scoop (2 Tbsp).
Bake at 350° for 9-11 minutes or until golden brown. Optional: Bang the cookie sheet against the counter a couple of times to flatten the cookies if they have domes. They are easier to dip in icing if the tops are flat. Let cookies to stand 2 minutes before transferring to a wire rack to cool completely.
While the cookies are cooling, make a batch of glaze. Stir milk, vanilla extract and powdered sugar together. Add water, 1 tsp. at a time until desired consistency is reached.
Quickly dip the top of each cookie in the glaze. DO NOT PRESS down, or submerge the cookie. You just want to coat the top surface. Allow excess to drip off.
Place the cookies back onto the cookie sheet or cooling rack while the icing hardens.
Video
Notes
Store cookies in an airtight container for 3-5 days. Cookies (with or without icing) freeze well.