Preheat oven to 180°C/350°F. Add 100g (7 tbsp) butter to a small saucepan and set over medium-high heat. Melt the butter, stirring or swirling occasionally, and cook until it begins to bubble, the bubbles subside and you notice the butter beginning to turn brown on the bottom of the pan. Remove from the heat, pour into a bowl and allow to cool to room temperature.
Meanwhile, in a medium mixing bowl, whisk together the flour, baking powder & soda and salt. Set aside.
Add the brown butter to the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl. Add the remaining butter, the caster sugar and the brown sugar. Using a stand or hand mixer, beat at medium speed until just combined. Scrape down the sides of the bowl and increase the speed to medium-high. Beat until it's light, creamy and aerated - 2-4 minutes.
Scrape down the sides of the bowl and add the egg and vanilla extract. Beat on medium until well combined and fluffy.
Scrape down the bowl and add the dry ingredients. Beat until just combined but some dry spots still remain. Finish mixing by hand using a silicone spatula.
Line two rimmed baking sheets with parchment paper. Portion the dough into 2 tbsp-sized balls and arrange on the baking trays -assuring there is ample space between. Flatten the dough balls so that they resemble discs about 4cm (1½in) wide. (See note 2)
Bake one tray at a time until the cookies are soft in the middle and dry and lightly crisp around the edges - 12-15 minutes. Transfer to a wire rack to cool completely
Notes
Because the volumetric measurement of salt can vary from type to type and brand to brand, I highly recommend using the weight measurement of salt in order ensure that the salinity is evenly balanced.
At this point, you can freeze the portioned-out cookie dough on the sheets. Once frozen solid, transfer to an airtight container and keep in the freezer for up to 3 months. You can bake directly from frozen, just add 3-5 minutes onto the baking time.