In a small saucepan, melt the butter over medium heat. Cook for several minutes to brown the butter. It will go from simmering to bubbling to foaming, and you will begin to see brown flecks on the edges of the pan and the bottom. It will smell nutty and delicious. Once you can see a good amount of brown specks, remove from heat and pour butter and scrape all the bits into a large glass mixing bowl that you will use for the cookies.
Now that the brown butter is in the mixing bowl, add sugars and stir for about 30 seconds to combine. Let sit for 5 minutes. Then add sourdough discard and stir to incorporate a bit. Then add egg and vanilla, and switch to a whisk, whisking mixture until it is cohesive.
In another bowl, whisk together flour, baking powder, baking soda, cream of tartar, nutmeg, and salt. Add half the flour mixture to the wet mixture, and stir with a spatula, about 15 times. Then add remaining flour and stir gently to incorporate until no dry streaks remain.
Cover and refrigerate for 45 minutes. When that time is up, preheat your oven to 375 degrees F. Prepare a sheet pan with parchment paper, and scoop 55 gram dough balls (I usually bake 8 cookies at a time). Roll your dough balls in the cinnamon sugar mixture so they are fully coated.
When you put the dough balls in the oven, turn heat down to 350 degrees F. Bake for about 12-13 minutes, until edges are a little bit brown and middles are still soft and they are puffed up. Set baking sheet on counter and use the back of a spoon to press down the middle of each cookie. This creates that irresisitble gooey texture.
Let cookies cool on pan for 5 minutes. This is important, as they will finish baking here. Then move cookies to a wire rack to cool. Top with a light sprinkle of flaky salt.