In the bowl of a stand mixer, beat butter and sugars until light and fluffy. Add in egg and vanilla and beat until combined.
Add in flour, baking soda, and salt beat until combined. Stir in chopped pecans.
Cover and refrigerate 30 minutes (or more).
Preheat oven to 350 degrees F.
Shape into 1″ balls (I used a 1 tbsp cookie scoop) and place a couple inches apart on lightly greased cookie sheets or parchment paper. Bake 10 minutes or until set (not glossy at all in the middle) and lightly browned at the edges. Cool before frosting.
Combine brown sugar and milk in a small pot over medium heat. Bring to a boil and boil 3-4 minutes, stirring constantly. Remove from heat and stir in butter.
Stir in 1½ cups powdered sugar and whisk or beat with a mixer until smooth. If frosting is too thin, add more sugar, but keep in mind it will firm up dramatically within a few minutes.
Spread each cookie with about 1 tbsp frosting and top with a pecan or chopped pecans. Let frosting set before storing.
Mothers Secret Recipes of Comfort Food & Culinary Inspiration from an Organic and Allergen-free Approach