Preheat oven to 375 degrees F. Prepare a muffin pan with liners. Using a fork, combine the flour, brown sugar, pumpkin pie spice, butter and salt to make the crumb topping. Set aside for now.
In a large bowl attached to a standing mixture with a paddle attachment combine the first 7 ingredients of your muffin cake, then slowly add your butter, egg, and yogurt. Mix on medium until thoroughly combined. The batter will be pretty thick at this point.
Add in your grated apples and the associated liquid and mix until combined. Then remove your bowl from the mixture and with a spatula mix in your diced apples.
Fill your muffin cups ½ way with half of your muffin batter. Then sprinkle a layer of your crumb mixture over the batter, and fill your muffin cups with the remaining muffin batter. Top with another layer of your crumb mixture.
Bake for 20 minutes, turn your muffin pan and then bake for another 10 minutes.
While your muffins are baking go ahead and prepare your glaze. In a small bowl using a fork mix your powdered sugar and apple cider until smooth. Remove your muffins from oven and let cool. Then drizzle your glaze on top.