Preheat the oven to 350 F degrees. Grease an 8x8-inch or 9-inch round pan with butter and line with unbleached parchment paper for easy cake removal.
To make the streusel: In a medium bowl, whisk together the flour, sugars, cinnamon, and salt. Add the butter and vanilla and using a fork, or your fingers, break the butter into the flour until crumbs form and you can squeeze the mixture together to form clumps. There should be no dry spots. You’ll end up with crumbs of different sizes. Set aside.
In a large bowl, whisk together the melted butter or oil, applesauce, eggs, maple syrup and vanilla until well combined
In a separate medium bowl: whisk together the flour, baking powder, baking soda, cinnamon, allspice, ginger, nutmeg and salt. Add the dry ingredients to the wet ingredients and mix until just combined; do not overmix. Fold in the chopped apples.
Pour the batter into the prepared pan; sprinkle with the streusel mixture. (See notes for other ways to do this.)
Bake for 40-50 minutes or until a tester comes out clean with just a few crumbs attached. Allow the cake to cool completely before glazing.
To make the glaze: In a medium bowl, whisk together the powdered sugar, vanilla, and milk. Start with a little bit of milk to loosen the glaze. At first it will seem like it’s not enough liquid, but it eventually becomes silky. You can always add more milk to thin it out. Drizzle the glaze over the cake. Feel free to use as little or as much as you like.