Preheat oven to 350 degrees (175 C). Line 2 baking sheets with baking paper (parchment paper). Do not grease the paper or cookies will spread.
In a thick-bottomed skillet, melt half of the butter over medium heat. Continue cooking, whisking frequently, for about - 1 to 3 minutes or until butter is lightly browned and has nutty aroma. Be careful not to burn the butter. Transfer to a large bowl and add remaining unmelted butter. Stir until combined. (If your butter melts completely, put it in the freezer for a few minutes until it has consistency of a firm yogurt or cream).
Take 1 tablespoon of dough (or 2 tablespoons for extra large, 4 inch / 10 cm diameter cookies) at a time and roll into balls. Place 2 inches apart on lined baking sheets. You can add more chocolate chips on top of each cookie to make them look pretty (optional). To prevent cookies from spreading too much, you can chill them at this point (optional).
* If you don't have cake flour at hand, you can substitute it with homemade cake flour. Add 2 tablespoons of cornstarch to a 1 cup measure. Fill up the rest with the all-purpose flour. This is your cake flour. You will need ¾ cup of this mixture for this recipe.