Adjust oven rack to upper-middle position and heat oven to 400 degrees. Spray 12-cup muffin tin generously with vegetable oil spray. or line with cupcake liners. Set aside.
Melt 2 tablespoons butter in a 12-inch skillet over medium-high heat. Add apples, dark brown sugar, cinnamon, and salt. Cook, stirring often until moisture has completely evaporated and apples are well browned about 7-9 minutes. Remove pan from heat and let cool for 10 minutes.
Whisk whole wheat flour, baking soda, baking powder, freshly ground nutmeg, salt, and the remaining 1 teaspoon of cinnamon together in a large bowl.
Whisk applesauce, apple cider, buttermilk, maple syrup, egg, and vanilla together in a separate bowl for about 30 seconds. Add cooled apples to the mixture.
Pour the wet ingredients into the dry ingredients. With a spatula fold everything together gently just until combined. The batter will be thick.
Spoon the batter into tin or liners filling them almost to the top. Bake for 14-16 minutes at 400°F until golden brown and a toothpick inserted in the center comes out with a few crumbs.
Let muffins cool in muffin tin on wire rack for 5-10 minutes. Remove muffins from tin to wire rack and let cool.