Preheat oven to 350.
Sift flour, baking soda, and salt and set aside.
In large bowl of electric mixer, cream the butter. Add vanilla and sugar and beat well. Add the egg and continue to beat for a few minutes, scraping the bowl as necessary and beating until mixture lightens in color. On low speed, gradually add the sifted dry ingredients, scraping the bowl and beating only until the mixture is smooth.
Use a slightly rounded teaspoonful of dough for each cookie -- make these a little smaller than the average cookie. Roll the dough between your hands to form round balls and place 2" apart on unbuttered cookie sheets.
With your fingertip, make a wide, round depression in the center of each cookie -- it should reach almost to the edge, but leave a rim.
Prepare the topping: Add 1/2 cup dark brown sugar and the sour cream in a small mixing bowl. With a rubber spatula stir until smooth. Stir in nuts.
With a small spoon, place some of the topping into the dent in each cookie. The topping should be mounded fairly high above the cookie -- it will melt a bit as it bakes.
Bake for 13-15 minutes; cool.