In large bowl cream butter and sugars. Beat in egg. Add pumpkin and vanilla. Combine the flour, baking powder, baking soda, cinnamon and salt; gradually add to creamed mixture. Stir in pecans.
Drop by rounded teaspoons 2 inches apart onto ungreased cookie sheets. Bake at 350 degrees for 11 to 13 minutes or until edges are lightly browned. Remove to wire rack to cool.
For the frosting
In a small pan bring brown sugar and butter to a boil. Cook and stir over medium heat for 1 minute. Remove from the heat; cool 10 minutes. Transfer to large bowl; beat in milk. Beat in confectioners sugar to achieve spreading consistency. Frost cookies. Makes 5 dozen