Make the dough: in a big bowl, beat together the butter, sugars, cream of tartar, salt, eggs, baking soda, and maple extract until fluffy.
Add the flour; beat until blended; refrigerate dough for about 30 minutes, to stiffen it and make it easier to shape.
Make the coating: combine the sugars in a shallow bowl or pie plate, or in a large plastic bag.
Drop the dough by the rounded tablespoonful into the coating, gently shake the pan to coat the balls, then roll them in your hands until they are smooth and round.
Place the balls on baking sheet that has been sprayed with cooking spray, about 1 ½ inches apart.
Bake in a 400° oven for 10-12 minutes, until they are very light golden brown; remove them from the oven and after 5 minutes, transfer them to a rack to cool.
Make the glaze: in a bowl, stir together the powdered sugar, maple syrup, cream, and extract to make a spreadable frosting.
Spread a thin layer over the cookies; let the glaze dry for several hours before packaging the cookies for storage.