First toast the black sesame seeds for 20-25 seconds. Pour black sesame seeds into a spice grinder or food processor. (I recommend a spice grinder.) Pulse until it has fully broken down into powder. Pour into a bowl.
Add all purpose flour and baking soda to the bowl. Mix until combined and set aside.
Brown butter in a small sauce pan. Heat butter over medium high heat until the butter melts and then lower it to low. Cook the butter until golden brown and small brown solids start to appear. Remove from the heat and set aside.
Combine granulated sugar and light brown sugar in a large bowl. Add the brown butter. Whisk with a stand mixer or hand mixer until just combined.
Add the eggs and whisk until a smooth creamy mixture forms (picture 2 above). Add the salt and vanilla extract and mix until just combined.
Add the dry ingredients from step 2 to the bowl and mix with a spatula until just combined.
Let the cookies rest in the fridge for 20 minutes.
Preheat the oven to 350 degrees F.
Prepare 2 baking sheets by lining them with parchment paper. Use a 2 tablespoon (medium sized) cookie scoop to scoop your cookie dough onto the prepared baking sheets. Make sure there are 2 inches of space between each cookie.
Bake for 10-12 minutes until the edges are light brown.
Rest for 10 minutes on the baking sheets and then another 10 minutes on a cooling rack before serving.
I would highly recommend using a spice grinder to break up the black sesame seeds. The food processor just doesn't get that fine powder you want, but I would use it if that's all you have. Another option is to use black sesame powder.