Combine apple cider and apples in a saucepan over medium-high; cover, and cook 10 minutes. Uncover, and cook 2 minutes. Remove from heat; cool 10 minutes. Pour apple mixture into a blender; process until smooth.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, cinnamon, and salt in a medium bowl; stir with a whisk.
Combine apple mixture, sugar, yogurt, oil, and egg in a medium bowl; stir with a whisk. Add yogurt mixture to flour mixture, and stir until combined.
Coat 2 (6-cavity) doughnut pans with cooking spray. Spoon batter evenly into 12 cavities. Bake at 350°F for 12 minutes or until doughnuts spring back when lightly pressed. Cool in pan for 2 minutes. Invert doughnuts onto a wire rack. Cool completely.
Combine tahini and maple syrup, stirring with a whisk. Add 2 teaspoons water; whisk until smooth. Spread glaze over tops of doughnuts. Let stand until glaze is set.
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