In a large bowl, whisk together flour, cinnamon, nutmeg, baking soda and salt. Set aside.
In the bowl of a stand mixer (or using a hand mixer), combine vegetable oil, brown sugar, granulated sugar, eggs and vanilla. Mix on medium speed until light in color and creamy in texture, about 2 minutes.
With the mixer on low, slowly add the flour mixture and mix until just combined (avoid over-mixing).
Using a rubber spatula, carefully stir in the chopped apples by hand. Again, avoid over-mixing.
Transfer batter to prepared bundt cake pan and bake for 55 to 70 minutes, or until a toothpick inserted in the center comes out with little to no crumbs. Cool cake in pan for 20 minutes and then invert on a wire rack to cool completely. Prepare glaze.
In a small saucepan over medium heat, combine the butter, brown sugar and milk. Whisk often until the butter is completely melted and the mixture begins to boil. Remove from heat and cool for 10 minutes.
Add the confectioners' sugar and vanilla. Whisk until smooth. Gently pour glaze in a circular motion over the cooled bundt cake and serve. Store cake covered at room temperature for up to 5 days.
Suggested tools for this recipe:Bundt cake pan, kitchen scale, stand mixer, apple peeler/corer, and small saucepanGreasing a bundt cake pan: I highly suggest using my magic cake pan release paste if you use an intricate bundt cake pan like I did. It works like magic and guarantees that none of the cake sticks to the pan. Use a pastry brush to get in to all the edges of the pan.Apples for baking a cake: I suggest using Granny Smith or Honeycrisp apples. They keep their texture and flavor during the baking process.Storing apple bundt cake: Store cake at room temperature for up to 3 days or in the refrigerator for 5 days.Freezing apple bundt cake: Apple bundt cake (without glaze) may be frozen is wrapped tightly with plastic wrap and aluminum foil. Store in the freezer on a flat surface for 1 to 2 months. Defrost in the refrigerator before bringing to room temperature and serving.