Preheat your oven to 350 degrees F (175 degrees C). Prepare a large baking sheet by lining it with parchment paper. This will ensure your cookies don’t stick and come off easily after baking.
In a medium skillet over medium heat, melt the unsalted butter. Once it starts to melt, whisk it consistently. Watch closely as it begins to crackle and foam, which is a sign that it's on its way to becoming brown butter.
After a few minutes, the butter will develop a golden color and a nutty aroma. Remove it from the heat as soon as it turns a deep brown, being careful to not let it burn.
Transfer the brown butter to a mixing bowl, scraping all those delicious brown bits in as well. Let it cool for about 5 minutes.
Using an electric mixer, combine the brown butter with brown sugar and granulated sugar until well blended, around one minute.
Add the eggs and vanilla, beating them in until the mixture is smooth and creamy, which should take about another minute.
Next, add the dry ingredients: whole wheat pastry flour, old fashioned rolled oats, baking soda, cinnamon, nutmeg, and salt. Beat on low speed until everything is just combined.
Use a medium cookie scoop (or your hands) to portion out the dough, making about one large tablespoon for each cookie. Place them on the prepared baking sheet, ensuring to leave at least two inches of space between each one.
Bake the cookies in the preheated oven for 10 to 13 minutes, watching closely until the edges turn golden brown. Once baked, allow them to cool on the sheet for a few minutes before transferring them to a wire rack to cool completely.
While your cookies cool, mix the powdered sugar, additional vanilla, and milk in a separate bowl to create the icing. Stir until smooth with no lumps remaining.
Once the cookies have cooled, spoon about two teaspoons of icing onto each cookie, spreading it slightly. Place the cookies back on the wire rack so the icing can harden. And there you have it—your delicious Old Fashioned Iced Brown Butter Oatmeal Cookies!
