Preheat oven to 300°F. Line 2 half sheet pans with parchment paper.
In the bowl of an electric mixer fitted with the paddle attachment, beat dark brown sugar, butter, and shortening at medium speed for 2 minutes. Add baking soda, cream of tartar, and salt. Beat mixture until combined. Beat in egg and vanilla. Scrape the bowl as needed. Add flour and mix until combined.
Using a small ice-cream scoop, drop dough onto lined sheet pans. Flatten slightly with your hand. Bake for 8 minutes or until golden brown around the edges. Allow the cookies to rest for 5 minutes on the sheet pans. Remove from pans to cooling racks.