Beat the butter and both sugars in a large mixing bowl until light and fluffy.
Add the egg and vanilla extract and mix well.
Mix the flour, salt, and baking soda in another bowl. Add the dry ingredients
to the batter and mix until well blended. Stir in the chocolate chips and
walnuts.
Drop the dough by small scoops 2 to 3 inches apart on an ungreased cookie
sheet. Flatten each scoop with the back of a spoon to about 3 inches in diameter.
Bake until the centers are still slightly soft to the touch, 11 to 14 minutes.
Let cool on the cookie sheet for 5 minutes, then transfer to racks to cool
completely.