Adjust oven racks to center position and preheat oven to 425°F. Spray two 6-cavity donut pans with nonstick cooking spray and set aside.
In a large bowl, whisk together whole wheat pastry flour and cornstarch. Whisk in brown sugar, baking powder, salt, cinnamon, nutmeg, and allspice until well blended. Stir in apple cider, buttermilk, eggs, butter, and vanilla until batter is smooth and combined, but do not over-mix. Evenly divide the batter between the prepared donut pans.
Bake for 7 to 9 minutes until the edges of the donuts begin to turn a light golden brown and the tops of the donuts spring back when lightly touched. Allow donuts to cool for 5 minutes in pans before turning them out onto a cooling rack.
In a medium bowl, combine the sugar and cinnamon. Place the melted butter in a shallow bowl. Dip one side of each donut in the butter, and then press into the cinnamon sugar. Serve warm or at room temperature.
The cornstarch lightens up the texture of the donuts, akin to using cake flour. If you prefer, you may omit the cornstarch and increase the flour to 2 cups.