Preheat oven at 350-degrees. In a large bowl, cream butter and sugars together until they are light and fluffy. Beat in the egg, pumpkin, and vanilla.
In a separate bowl, sift together the flour, baking powder, baking soda, cinnamon and salt. Gradually mix the dry ingredients into the wet. Fold in the pecans.
Spread parchment paper on two large baking sheets. Drop dough by rounded teaspoon scoops spaced out to allow for a small amount of spreading. Bake for 9 to 11 minutes. Move cookies to wire racks to cool, which won't take long.
Meanwhile, in a small saucepan, bring the brown sugar and butter to a boil. Keep on medium heat for 1 minute, continuing to stir, then remove from heat. Cool for 10 minutes. Transfer to a larger bowl and beat in the milk. Slowly add in enough confectioners' sugar to reach a spreadable consistency. Immediately frost cookies. Let set for an hour or so before packing up.
Makes about 60 cookies. Best eaten within 1 day; they will still taste okay after that, but will soften more. Store cookies between wax paper layers in sealed containers.
OM NOM NOM!