Preheat the oven to 350°F (175°C). Grease and line an 8×8 square pan with parchment paper for easy removal.

In a small saucepan over medium-low heat, combine the butter and ⅔ cup of the sugar. Stir frequently until the butter is melted and the mixture looks glossy and smooth; let it cool slightly.

In a separate bowl, whisk together the eggs with the remaining 1 cup of sugar vigorously until the mixture starts to foam and is well-combined.

Gradually whisk the cooled butter mixture into the egg mixture. Make sure the butter is not too hot to avoid cooking the eggs.

Sift the all-purpose flour, cocoa powder, and salt over the batter, or whisk them together in a separate bowl before adding to avoid lumps. Mix gently until fully incorporated, ensuring no flour streaks remain.

Fold in the chocolate chips, then pour the batter into the prepared pan. Sprinkle additional chocolate chips on top if desired.

Bake for 30 to 35 minutes, until the top is set and has a few cracks. Be careful not to overbake, as this can lead to dry brownies.

Allow the brownies to cool completely on a wire rack. To unmold, gently pull the brownies out of the pan using the parchment paper overhang, then transfer to a serving plate. Cut into squares and serve.