In a heavy-bottom sauce pan, melt the butter over medium heat. Continue heating & whisking until the butter turns browns. Remove from the heat and allow to cool.
In a medium bowl, whisk together the flour, cinnamon, nutmeg, baking soda and salt for about 20 seconds. Set aside.
In a large bowl or the the stand of your electric mixer, beat the brown butter & sugars on medium speed until combined. Then add in the vanilla & eggs and continue mixing for about 30 seconds.
Scrape down the sides of your bowl. Slowly add in the flour mixture beating low speed until almost combined. Turn off your mixer, scrape down the sides of your bowl, and gently fold in your oats. The batter will be thick, so you may want to finish mixing by hand with a wooden spoon.
Form dough into 2 tablespoon balls. You should get about 40 cookies. Cover with clingfilm, and chill dough in the refrigerator for at least 1 hour (or up to 3 days).
Preheat the oven to 350F degrees. Remove dough from the fridge and place on baking sheets lined with parchment paper or a silicone baking mat.
Bake for 8-10 minutes (mine took exactly 8 minutes), until cookies are slightly browned on the edges. Leave to cool on the tray for about 3-5 minutes, then transfer to a wire rack to continue cooling.