COOKIES: In a large bowl, beat together butter and sugars, until light and fluffy. Add egg and vanilla, beat until combined.
In a separate bowl, combine flour, baking soda, and salt. Add dry ingredients to wet ingredients, beat until combined. Stir in a 1/2 cup chopped pecans. Cover and refrigerate for 1 hour or more.
Preheat oven to 350 degrees. Line baking sheets with parchment paper; set aside.
Using a tablespoon or cookie scoop, shape cookie dough into 1-inch balls and place 2-inches apart on prepared baking sheets. Bake for 10 minutes or until set and lightly brown around the edges. Cool before frosting.
FROSTING: Sift confectioner's sugar into a large bowl; set aside.
In a small saucepan, over medium heat, bring brown sugar and cream to a boil. Boil 3-4 minutes, stirring constantly. Remove from heat and stir in butter.
Pour brown sugar mixture over confectioners' sugar, beat with an electric mixer until smooth.
Immediately spread each cookie with about 1 tablespoon of frosting, and top with a pecan or chopped pecans. Let frosting set before storing.