Preheat oven to 400°F. Coat a 12-cup muffin tin with cooking spray.
Whisk 1¼ cups all-purpose flour, ¾ cup whole-wheat flour, 1 tablespoon baking powder, 1¼ teaspoons cinnamon and ½ teaspoon each baking soda, allspice and salt in a medium bowl until combined.
In a large bowl, whisk 1¼ cups yogurt, ½ cup applesauce, 2 eggs, 4 tablespoons brown sugar and 2 teaspoons vanilla until well combined.
Add the flour mixture; stir until nearly combined. Fold in 1 cup apple just until evenly distributed.
In a small bowl, stir together 6 tablespoons oats and the remaining 5 tablespoons all-purpose flour, 1 tablespoon brown sugar and ¼ teaspoon cinnamon. Add the melted butter; stir until the mixture is crumbly.
Divide the batter among the prepared muffin cups. Sprinkle the streusel over the batter.
Bake for 5 minutes. Without opening the oven, reduce oven temperature to 375°F. Bake until the muffins are golden brown and a wooden pick inserted in the centers comes out clean or with a few moist crumbs, 14 to 18 minutes.
Let the muffins cool in the pan for 5 minutes. Transfer to a wire rack and let cool for 20 minutes. Serve warm or at room temperature.
