In large bowl, stir baking mix, 1/4 cup of the sugar, the ginger and pumpkin pie spice. In small bowl, mix milk, molasses and eggs. Add milk mixture to dry ingredients, stirring until smooth.
In deep fryer or 3-quart heavy saucepan, heat oil to 350°F. In small bowl, mix remaining 1/2 cup sugar and the cinnamon; set aside. Drop batter by tablespoonfuls into hot oil; cook 2 minutes, turning once, until brown. Drain on paper towels; roll warm doughnut holes in cinnamon-sugar.