In a large mixing bowl, beat butter with an electric mixer for 30 seconds. Add the 1-1/2 cups sugar and pumpkin. Beat until combined.
Beat in vanilla, cream of tartar, baking soda, and salt. Beat in egg. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Cover and chill 1 hour.
In a small mixing bowl, stir together the 1/2 cup sugar and cinnamon. Drop cookie dough by teaspoonfuls into the sugar-cinnamon mixture, rolling to coat. Place cookies 2 inches apart on ungreased cookie sheets.
Bake in a 350 degree F oven about 10 minutes or until edges are golden. Remove and cool on wire racks.