Preheat the oven to 350 degrees Fahrenheit. Then mix brown sugar, egg, and lemon oil together in a bowl until creamy. Stir in the flour, baking soda, cream of tartar, ginger, and salt until the dough comes together. Pour white sugar onto a plate. Roll dough into 1-inch balls; dip one side in white sugar. Arrange balls, sugared-side up, on 2 baking sheets. Bake in the preheated oven for 10 to 12 minutes, until edges are pale golden and tops look dry.