I start by pouring the apple cider into a small saucepan and letting it simmer over medium heat. It takes about 20 minutes to reduce down to a concentrated 1/4 cup. This step matters because plain cider is too watery to add real flavor to the batter. Once it's reduced, I let it cool for at least 10 minutes before moving on.
While the cider cools, I whisk together the flour, baking powder, baking soda, salt, and all the spices in one large bowl. Getting the spices evenly distributed here means every bite of the finished muffin tastes balanced. I set this bowl aside once everything looks combined.
In a separate bowl, I whisk the oil, both sugars, eggs, applesauce, and the cooled cider reduction together until smooth. This mixture should look glossy and well blended before you move to the next step. There's no need for a stand mixer at any point in this recipe.
I pour the wet mixture into the dry ingredients and whisk just until combined, being careful not to overmix. Then I gently fold in the shredded apple and walnuts if I'm using them. The batter will look thick and a little chunky, which is exactly right.
I divide the batter evenly among the muffin liners, filling each one all the way to the top. Baking starts at a high 425°F for 5 minutes, then I drop the oven down to 350°F for another 15 to 16 minutes. That initial blast of heat is what gives the muffins their tall, bakery-style dome.
Once the muffins are baked, I let them cool in the pan for about 10 minutes. Then I brush the warm tops with melted butter and roll them in a cinnamon-sugar mixture. This final touch is what makes these taste like apple cider donuts in muffin form.