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In a medium saucepan combine apples, granulated sugar, cinnamon, nutmeg, cornstarch and water. Heat over medium heat for5-6 minutes until apples soften and a liquid thickens. Set aside to cool.
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Mix dark brown sugar and cinnamon in a small bowl and set aside.
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Cake
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Preheat oven to 350°
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Spray a 9x13 pan with baking spray.
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In your mixing bowl beat butter and sugar, about 3 minutes until fluffy. Add applesauce, vanilla and eggs and mix on medium until combined.
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In a separate bowl whisk together flour, baking powder, baking powder, salt and cinnamon.
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Add the dry mixture and the Greek yogurt in alternating parts, starting and ending with the dry.
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Mix until just combined.
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Spread 1/2 the cake batter in the bottom of the prepared pan. Top with the apple mixture, spreading carefully to cover the batter. Then top with 2/3 of the brown sugar, sprinkling all over the apple mixture.
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Cover with the remaining batter and sprinkle the remaining 1/3 of the brown sugar all over the top.
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Bake 35-40 minutes, or until the center of the cake is set.
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Glaze
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While the cake is baking prepare the glaze by mixing the powdered sugar, milk and vanilla in a medium bowl.
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When cake is done, immediately poke holes in the cake using a butter knife, about 30 pokes.
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Pour the glaze over the top of the cake spreading to cover it completely.
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Let the glaze set up for about 20 minutes before serving.