In the bowl of a stand mixer fitted with the paddle attachment, cream butter, coconut sugar and ¼ cup/50 grams maple sugar on medium speed until light and fluffy, 3 to 4 minutes. Add the eggs one at a time and mix until well incorporated after each addition, scraping the bowl as necessary. Beat in the vanilla extract.
Add the flour mixture and mix on low speed until incorporated. With the mixer running, add the apple juice in a slow, steady stream and mix to combine.
Spoon or pipe the batter into prepared doughnut pans, filling them 7/8 of the way, almost to the top. (You can also do this using a disposable piping bag or a resealable plastic bag with a ½-inch opening cut from one corner.)
Bake until evenly golden brown and a toothpick inserted into the center of the thickest portion comes out clean, 15 to 17 minutes. Rotate the pans halfway through baking. (If you are making muffins, divide batter evenly between the prepared cups and bake for 20 to 25 minutes, rotating halfway through.)
While the donuts bake, blend the remaining ½ cup/100 grams maple sugar and 1 teaspoon cinnamon in a mini food processor or clean coffee grinder. Cool the donuts for 5 minutes on a wire rack then unmold them from the pans and dredge them in the cinnamon sugar while they are still warm. Serve immediately, or let cool to room temperature.
Notes
If sugar mixture isn’t sticking to the donuts, brush them lightly with a bit of apple juice before dipping.