Place the butter in a saucepan over medium heat. (Optional - cut the butter into tablespoon-sized pieces to melt it more easily). Melt the butter in the saucepan while stirring occasionally. When it has melted and starts to bubble, use a spatula to stir the butter mixture more frequently to prevent milk solids from sticking to the bottom of the pan.
Keep heating the butter until it stops bubbling. After a while, you will see white milk solids at the bottom of the pan. Keep cooking the butter and stirring, until the milk solids turn a dark golden brown. This will happen very quickly once the milk solids turn light brown in color first, so keep stirring and don’t leave the pan unattended at this stage, to prevent the butter from burning.
As soon as the milk solids turn dark golden brown, pour the butter into a measuring cup and let it cool to room temperature (ideally about 75°F)
When the butter is at room temp., add just enough water to make 1 cup of liquid. (About 1 - 1½ tbsp)
Place the cooled butter and water into the bowl of your stand mixer (or a large bowl for a hand-held mixer). Add both sugars, salt and vanilla, and mix on medium speed ONLY until the butter-sugar mix becomes creamy and a shade lighter (see pictures in post). This is important, as it prevents the cookies from being greasy once baked. DO NOT MIX TOO MUCH, if you add more air, the cookie dough will end up needing more flour.
Add the eggs, and mix until just mixed through. The cold eggs will bring the temperature of the dough down as well.
In a separate bowl - sift the flour, baking soda and baking powder together. Add the flour in two additions while the mixer is on the lowest speed. This is to prevent the flour from flying everywhere and making a mess, and also to prevent the dough from being over-mixed. The flour doesn’t have to be completely mixed in before adding more.
When most of the flour is mixed in, add the chocolate chunks/chips, and mix on low speed until the chocolate chunks/chips are mixed through. Remove the bowl from the mixer, and let the mixture rest for at least 15 minutes, ideally 30 minutes, covered. IF the dough is too soft, let the dough rest in the fridge. It will harden up as it rests.
Using a 3 tbsp cookie scoop, portion the cookie dough out onto a parchment paper-lined half sheet pan. Don't worry about spacing, as this is just to chill the cookie dough first.
OPTIONAL - Add a few pieces of chopped chocolate ontop of each of the cookie portions. These will give the pools of chocolate as the cookies bake. It's easier for the chocolate to stick to the dough while it's still soft.
If you want to bake the cookies right away, you can do so (but the cookies will spread thinner). But for best results, I'd recommend covering the sheet pan with plastic wrap and letting the cookie dough chill overnight (or at least 1 hour).