Preheat the oven to 350°F. Cream together butter and sugar until smooth and combined. Mix in the egg and vanilla. Sift the flour, baking soda, and salt. Add to the wet ingredients.
In a separate bowl combine the chopped walnuts, ½ cup of brown sugar and the sour cream.
Using a 1½ inch cookie scoop place scoops of dough on a silpat or parchment lined baking sheet. Make a thumbprint indentation into each cookie and fill with a generous teaspoon of the walnut filling.
Bake for 11-12 minutes until just starting to turn brown. Remove from the oven and let cool for 5 minutes on the baking sheet. Place cookies on a wire rack to finish cooling.