Preheat oven to 325°F (163°C). Spray a bundt pan well with nonstick cooking spray and set aside.
In a large mixing bowl, whisk together the flour, ground cinnamon, ground allspice, baking soda, and salt. Set aside.
In a separate large mixing bowl, whisk together the oil, granulated sugar, brown sugar, eggs, and vanilla extract until fully combined. Add the dry ingredients and mix until just combined, the batter will be pretty thick at this point.
Add the chopped apple and gently fold it into the cake batter. Scoop the batter into the prepared bundt pan and spread it around into one even layer.
Bake at 325°F (163°C) for 60-65 minutes or until a toothpick inserted into the cake comes out clean. Tent with foil for the last 10-15 minutes of baking if needed to prevent excess browning.
Remove from the oven and place on a wire rack to cool for 20 minutes, then carefully flip onto the wire rack, remove from the pan, and allow to cool completely.
To make the vanilla glaze:
Whisk together the powdered sugar, milk, and vanilla extract until no lumps remain. If the glaze is too thin, add more powdered sugar. If the glaze is too thick, add more milk until it has reached your desired consistency.
Drizzle on top of the cooled apple cake and set aside for 15-20 minutes to harden.
Store leftover apple cake in an airtight container at room temperature for 2-3 days or in the refrigerator for up to 5 days.To make in loaf pans: Spray two 9x5 loaf pans with nonstick cooking spray. Evenly divide the batter between both loaf pans and spread around into one even layer. Bake at 325°F (163°C) for 60-65 minutes or until a toothpick inserted into the center comes out clean. Tent with foil for the last 10-15 minutes of baking time if needed to prevent excess browning on top.Freezing Instructions: Cake will freeze well for up to 3 months. Thaw overnight in the refrigerator and bring to room temperature before serving.Apples: I suggest peeling your apples. I used Honeycrisp apples in this cake, but some other great options are Fuji or Gala apples.