In a mixing bowl, mix together oats, flour, whole wheat flour, baking powder, baking soda, salt, cinnamon and nutmeg until combined.
Using a stand mixer and paddle attachment or electric mixer, whip butter, granulated sugar, and brown sugar until pale and fluffy (about 3 minutes). Add eggs one at a time; mix until incorporated, add vanilla.
Add the dry ingredients and mix until just combined. Cover and refrigerate dough for at least 3 hours or up to 24 hours.
When ready to bake, preheat oven to 350°F. Line a baking sheet with parchment paper, if desired.
Scoop dough by heaping tablespoons and roll (roughly) into a ball. Place on baking sheet and bake for 12 to 13 minutes. Cookies will not be browned. If you prefer a crisper cookie, bake 1 to 2 minutes longer.
Cool on baking sheet for a few minutes before moving to a wire rack to cool completely.
Make Icing: In a shallow bowl, blend together powdered sugar and milk. Add just enough milk so that you’re able to dip the cookies in and have the icing stick to the cookies. It should be thick but not too thick.
Dip tops of cookies lightly in icing, giving them a little twist, and return them to wire rack. Tops of cookies should be lightly iced, with some cookie showing through. Allow icing to set before storing in an airtight container.
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Notes
Cookies can be stored at room temperature for up to a week; in the refrigerator for a couple of weeks, or in the freezer for up to 6 months.
The all-purpose flour and whole wheat flour can be added in any ratio. You can use 100% of either flour.
To store cookie dough: Wrap it securely and refrigerate for three to five days. To freeze, wrap and put into a freezer safe container for up to 2 months. If you prefer, roll the dough in balls before freezing. Freeze the individual dough balls separately on a tray for an hour or until they are firm, then transfer to a freezer safe container. You can bake them right from the freezer, adding a minute or two to the baking time.