Heat oven to 350°F. Line 15 muffin cups with paper baking cups. Reserve 1 tablespoon of the brown sugar in the muffins for filling.
In large bowl with electric mixer, mix remaining brown sugar for muffins, 1 3/4 cups flour, the baking powder, cinnamon and salt on low speed until mixed. Reserve 1 tablespoon of the beaten egg for filling. Add oil, applesauce, vanilla and remaining egg to flour mixture. Beat on medium speed until mixed. With spoon, stir in apple.
In small bowl, mix cream cheese, the reserved 1 tablespoon brown sugar and reserved 1 tablespoon egg. Fill muffin cups slightly less than half full of batter. Top each with 1 teaspoon cream cheese mixture. Top with spoonful of remaining batter to fill cups 2/3 full. In small bowl, mix all streusel ingredients; sprinkle over batter.
Bake 22 to 26 minutes or until toothpick inserted in center comes out clean. Remove from pan. Cool slightly, about 10 minutes.