Preheat the oven to 350 degrees F. Spray four 6-cavity donut pans with nonstick baking spray.
In a large mixing bowl, combine the flour, baking powder, salt, cinnamon, nutmeg and lemon zest. Whisk for 30 seconds to distribute the leavening.
In a liquid measure cup, combine the cider, buttermilk and vanilla.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter, brown sugar and granulated sugar. Mix on high until light and fluffy, 3 to 4 minutes. Scrape down the bottom and sides of the bowl.
Add the eggs, one at a time, mixing well between each addition. Scrape the bottom and sides of the bowl.
With the mixer on low, add one-third of the flour mixture and then half of the cider mixture. Continue alternating between the two until the batter is just combined. Remove the bowl from the stand mixer and, using a large rubber spatula, fold the batter a few times to make sure the ingredients are well distributed.
Transfer the batter to a piping bag or a large zip-close bag with a corner snipped off, and pipe into two of the donut pans. Top each pan with a second, inverted pan and use clips to hold them in place. (Some pans come with clips; otherwise, use metal hardware or paper clips.) Bake until the cake just springs back when gently touched, 15 to 20 minutes.
Turn the donuts out onto a cooling rack; immediately brush with melted butter, then dip in the cinnamon sugar.