Preheat your oven to 350ºF (175ºC).

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.

Add in the egg and vanilla extract, beating until fully incorporated.

In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add this mixture to the wet ingredients, mixing until a uniform dough forms.

Fold in the finely chopped pecans.

On a greased baking sheet, place 1-inch balls of dough, leaving space between them.

Bake for 10-12 minutes, or until the edges are lightly golden brown.

Allow the cookies to cool completely before frosting.

In a saucepan, combine 1 cup of brown sugar, 1/2 cup of milk, and 1 tablespoon of butter. Cook over medium heat until it comes to a boil, stirring continuously.

Remove from heat and gradually whisk in 2-3 cups of powdered sugar until smooth and spreadable.