In a large bowl, combine the cake flour, baking powder, baking soda, salt, cinnamon, allspice, and nutmeg. Set aside.

In a small saucepan, place the apple cider concentrate and butter over low-medium heat until the butter is fully melted. Remove the pan from heat.

Vigorously whisk in the brown sugar until fully dissolved, then pour the mixture into a large bowl.

Quickly whisk in the egg and vanilla. Then, mix in half of the dry ingredients until barely combined, followed by the applesauce and sour cream. Add in the remaining dry ingredients and gently fold with a rubber spatula until just combined.

Cover the bowl and place in the fridge to chill for at least one hour or overnight.

Just before rolling out the dough, fill a dutch oven or heavy bottomed pot with enough vegetable oil to cover 2” (5 cm). Heat the oil over low-medium heat and bring to 350 degrees F (180 degrees C).

Place a wire rack over a paper towel lined baking sheet. On a separate baking sheet, cut out 13 4” (10 cm) parchment squares for the donuts.

Meanwhile, make the coating. In a small bowl, melt the butter and stir in the apple cider concentrate. Set aside. In another medium bowl, combine the sugar and cinnamon.

Roll the dough out between two pieces of well floured parchment paper to ½” (1.25 cm) in thickness. Brush away any excess flour.

Use well floured 3” (7.5 cm) and 1” (2.5 cm) round cutters to cut out as many donuts as possible and place each on a parchment square. Re-roll the dough and cut out more donuts as needed.

Use the parchment squares to gently lower 2-3 donuts into the hot oil. Fry the donuts for 3 minutes on the first side, then flip over and fry for an additional 2 minutes.

Transfer the donuts to the wire rack. Wait a couple minutes for the oil to come back up to 350 degrees F (180 degrees C), then continue frying the donuts.

Once the donuts have cooled just enough to handle, brush the butter cider mixture on the top of each donut. Then, toss them in the bowl of cinnamon sugar to coat.