Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a medium bowl, cream together the butter and 1 cup brown sugar until smooth. Beat in the egg and stir in the vanilla. Combine the flour, baking soda and salt; stir into the sugar mixture. Roll the dough into 1 inch balls and place them 2 inches apart onto the prepared cookie sheets. Make a depression in the center using the cap from the vanilla or the end of a wooden spoon. Mix together the pecans, sour cream and 1/4 cup brown sugar; fill each depression with the mixture.
Bake for 8 to 11 minutes in the preheated oven, or until light brown. Cool for a few minutes on the cookie sheets before removing to wire racks to cool completely.