Preheat the oven to 350 degrees and spray a mini bundt pan (the kind with 6 wells) with cooking spray. (Alternatively, make cupcakes and line a muffin pan with liners). Set aside.
Place the pecans on a baking sheet and bake for 8-10 minutes or until lightly golden brown and fragrant. Set aside.
Mix the flour, sugars, cinnamon, xanthan, salt, baking soda, nutmeg and allspice in the bowl of a stand mixer fitted with a paddle attachment. Add the eggs, oil, apple sauce, and vanilla and beat until smooth. Gently mix in the apples and pecans by hand.
Spoon the mixture equally into the wells of your prepared pan and bake for 18-20 minutes or until a toothpick inserted in the center of one of the cakes comes out clean. Cool in the pan for 5 minutes, then turn out onto a rack to cool completely.
Make the glaze. Heat the butter and brown sugar together in a medium saucepan. Boil for 1 minute, whisking constantly, and remove from heat. Stir in the milk, vanilla and powdered sugar and beat with a whisk until smooth. Drizzle the glaze evenly over the cakes.