Prepare the Pan: Heat the oven to 325°F and line a metal 8 × 8-inch baking pan with parchment paper.
Melt the Butter: Melt the unsalted butter, preferably in a small skillet or saucepan over the stovetop, until it reaches a very low simmer. Use it while it is still hot rather than allowing it to cool.
Blend the Sugars: Add the hot melted butter, granulated sugar, and brown sugar to a large mixing bowl. Mix vigorously for 1 minute, until the mixture becomes less grainy and the sugar is thoroughly saturated with butter.
Incorporate the Eggs: Add the eggs to the butter-and-sugar mixture and stir thoroughly until the batter is smooth and the eggs are completely incorporated.
Add the Dry Ingredients: Add the all-purpose flour, cocoa powder, kosher salt, and vanilla extract. Stir just until the ingredients are combined, avoiding unnecessary mixing.
Fold in the Chocolate Chips: Set aside a handful of the chocolate chips for the topping. Stir the remaining chips into the batter until they are evenly distributed and no dry pockets of flour or cocoa remain.
Fill the Pan: Transfer the brownie batter to the prepared pan. Use a spatula or offset spatula to spread it evenly into the corners and across the surface.
Add the Topping: Scatter the reserved chocolate chips evenly over the top of the brownie batter.
Bake the Brownies: Bake at 325°F for 45–50 minutes. The finished brownies should have a glossy, crinkly surface with several small, hairline cracks beginning to form.
Cool Before Slicing: Let the brownies cool in the pan for at least 30 minutes. Transfer them to a cutting board or wire cooling rack and allow them to cool completely before slicing for cleaner portions.