I start by preheating my oven to 350°F so it's fully hot by the time the batter is ready. Then I coat the inside of the bundt pan generously with nonstick spray and dust it with a light layer of flour. This step matters more than people think, since a bundt pan's grooves can easily trap cake if it isn't prepped well.
In my large bowl, I sift in the flour first to keep the crumb light, then whisk in the brown sugar, granulated sugar, cinnamon, nutmeg, baking powder, baking soda, and salt. Whisking everything together evenly means I won't get a bite with too much baking soda or not enough spice.
In a separate medium bowl, I whisk together the apple cider, applesauce, oil, eggs, and vanilla until it looks smooth and well blended. I make sure my eggs aren't cold from the fridge, since that can cause the oil to separate slightly.
I pour the wet mixture into the dry ingredients and whisk just until combined. I stop as soon as I don't see streaks of flour, because overmixing here is what leads to a denser, tougher cake instead of a tender one.
I pour the batter into my prepped bundt pan and bake for 40 to 45 minutes. I start checking around the 40-minute mark with a toothpick inserted into the center, and I pull it out once the toothpick comes out clean or with a few moist crumbs.
Once it's out of the oven, I let the cake cool in the pan for about 15 minutes before turning it out onto a cooling rack. I then let it cool for another 20 to 30 minutes so it's sturdy enough to handle the coating without falling apart.
I mix the melted butter with the two tablespoons of apple cider, then brush this all over the cooled cake using every last drop. Right after that, I sprinkle on the cinnamon sugar mixture and press it gently into the surface with my hands.
Right before serving, I whisk the powdered sugar with the apple cider, adding it a teaspoon at a time until it's pourable but not watery. I drizzle it generously over the top and let it drip down the sides for the prettiest presentation.