Preheat the oven to 350 degrees F. Grease a 9-inch round springform pan, line the bottom with parchment paper, then grease once more. Set aside.
In a medium bowl, whisk together the white whole wheat flour, all purpose flour, cinnamon, baking soda, salt, all spice, and nutmeg. Set aside.
In a large mixing bowl, cream together the butter and granulated sugar until light and fluffy. Beat in the egg and vanilla extract.
Add 1/3 of the dry ingredients to the bowl with the butter, then 1/2 of the buttermilk, stopping to combine after each addition. Repeat, adding the second 1/3 of the dry ingredients, the remaining 1/2 of the buttermilk, and ending with the remaining 1/3 of the dry ingredients. Scrape the bottom and sides of the bowl to make sure everything is evenly combined. Stir in the apples. Scrape the batter into the prepared baking pan, then with the back of a rubber spatula, smooth the top.
Next, prepare the streusel topping. In a small bowl, combine the oats, brown sugar, cinnamon, and salt. Pour in the melted butter, then stir until the mixture forms large crumbs. Stir in the nuts. Sprinkle the streusel over the coffee cake batter in the pan.
Bake the coffee cake for 25 to 30 minutes, until the top is light golden brown and a toothpick inserted in the center comes out clean. Let cool in the pan on a wire rack for 20 minutes. Run a butter knife around the cake’s edges to loosen it, then unmold.
Last, prepare the glaze. Whisk together the powdered sugar, milk, and vanilla extract until smooth. Drizzle over the warm cake after it has been unmolded. Enjoy warm or at room temperature.
TO STORE: Keep leftover apple coffee cake in a tight container at room temperature for up to 4 days.
TO FREEZE: Wrap the coffee cake, unglazed, in plastic and freeze for up to 1 month. Let thaw overnight in the refrigerator, then glaze just before serving.