Position racks in the upper and lower thirds of the oven; preheat to 400 degrees F. Whisk the flour, cream of tartar, baking soda, baking powder and salt in a medium bowl. Beat the butter and 3/4 cup granulated sugar in a large bowl with a mixer on medium-high speed until fluffy, about 3 minutes. Beat in the egg, then the molasses and orange zest. Reduce the mixer speed to low; beat in the flour mixture until just combined.
Combine the cinnamon and the remaining 3 tablespoons granulated sugar in a small bowl. Roll heaping tablespoonfuls of dough into balls, then roll in the cinnamon sugar to coat. Arrange 2 inches apart on 2 ungreased baking sheets. Sprinkle with coarse sugar.
Bake, switching the pans halfway through, until the cookies are just set around the edges but the centers are still soft, 11 to 13 minutes. Let cool 3 minutes on the baking sheets, then transfer to racks to cool completely.