Preheat oven to 350°F (175°C).
In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the egg and vanilla extract, and mix until combined.
In a separate bowl, whisk together the flour and baking powder. Gradually add to the butter mixture, mixing until just combined.
Fold in the chopped pecans.
Drop spoonfuls of dough onto a baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are lightly golden. Let cool on a wire rack.
For the icing, brown the butter in a saucepan over medium heat. Remove from heat and let cool slightly.
In a bowl, whisk together the browned butter, powdered sugar, milk, and vanilla extract until smooth.
Spread the icing over the cooled cookies.