Use a fork to cut together all ingredients for crumble topping in a large bowl (the mixture will look like large crumbs); set aside.
For the Cake:
Preheat oven to 350F; butter and flour a 9-inch springform pan.
In a medium bowl, whisk together the flours, baking powder, baking soda, cinnamon, nutmeg, and salt; set aside.
In a large bowl, beat together the butter and sugars; then beat in the eggs until light and fluffy. Beat in the milk and vanilla. Gradually stir the dry ingredients into the wet, then fold in the shredded apple, being careful not to over-mix.
Spread ⅔ of the batter in an even layer in the bottom of the prepared pan. Add the pears and spread in an even layer, leaving a rim along the outside of about ¼ inch. Spread the remaining ⅓ of the batter evenly on the top of the pears. Sprinkle on the crumble topping.
Bake until a toothpick inserted in the center comes out clean, about 50 to 60 minutes. Cool completely, then dust with powdered sugar (if using) and serve.