1. In a large bowl, use an electric mixer on medium-high to beat eggs, brown sugar, and 1/4 cup sugar until light, about 30 to 60 seconds. Blend in 3 Tbsp. of the oil, then cider or juice, applesauce, and apple butter until combined.
2. In a separate bowl, stir together both flours, baking powder, baking soda, salt, nutmeg, and 1 tsp. of the cinnamon. Slowly stir the dry ingredients into the wet ingredients until mixed; dough should be similar to cookie dough. If it's very wet, add additional flour 1 Tbsp. at a time.
3. On a work surface, lay out a long sheet of plastic wrap. Scoop half the dough onto the plastic and pat into a rectangle about 1 inch thick. Wrap and freeze 30 minutes or refrigerate overnight. Repeat with remaining dough.
4. When ready to cook, pour remaining oil as needed into a deep frying pan or stockpot, to a depth of 1 inch. Heat oil on high until it reaches 335 degrees F to 340 degrees F on a deep-fry thermometer, about 8 to 10 minutes.
5. In a small bowl, combine remaining 1/2 cup sugar and 1 tsp. cinnamon and mix well; set aside. Line a cooling rack with paper towels.
6. While oil heats, roll out chilled dough on a floured work surface into a rectangle about 3 to 4 inches wide and just under 1/2 inch thick. Cut the rectangle widthwise into 1/2-inch-long strips. Lightly roll each strip into a snake and form it into a ring, securing the ends. There should be about 22 rings. Stretch rings if needed so hole is 1 to 11/2 inches wide. Transfer rings to a plate and repeat with second piece of chilled dough.
7. When oil has reached 335 degrees F, carefully place doughnuts in the hot oil, 4 to 6 at a time, leaving at least 1 doughnut's worth of space empty. Fry for 60 to 75 seconds, turn, and fry the second side for 45 to 60 seconds, until the doughnuts are a dark golden brown. Use a slotted spoon to transfer cooked doughnuts to the rack. Keep the oil at a constant temperature while frying; monitor and adjust the heat if needed. Add additional oil to maintain depth and heat to the proper temperature if needed.
8. When all the doughnuts are cooked, roll in cinnamon sugar and serve.
Source: Hannaford fresh Magazine, November - December 2012