Do not use an electric mixer. This whips too much air into the batter, which results in cake-y cookies.
Let the butter soften first at room temperature for about 1 hour.
Mix dry ingredients together in a separate bowl with a whisk.
Use a wooden spoon to stir the softened butter, but not too much. Add your sugar and stir until incorporated. Add egg and vanilla and stir well.
Add dry ingredients in 3 increments, stirring after each addition with your wooden spoon until blended. Finally, add chocolate chips and chopped walnuts.
Spoon onto cookie sheet, bake in preheated 375 degree oven until brown, about 9 minutes, and then cool on rack.
To make cookies extra crispy and with an even better texture, substitute 1/8 cup of the flour with 1/4 cup oats, ground in a coffee grinder or food processor until fine but not powdery (about 5 seconds).
Use a Silpat (French silicone baking mat) for really great crispiness without danger of burning the bottoms of the cookies.
Wear oven mitts when taking out cookies . Be careful not to burn yourself if you have rubber mitts.