Place the mandarins in a 2-quart pot. Fill the pot with 1 ½ quarts of filtered water. Bring the mixture to a boil over medium-high heat, and boil for 30 minutes. Flip the mandarins over and boil until soft, 30 minutes more. Drain the mandarins in a strainer and transfer to a small bowl. Using a fork, pull apart the skins and remove and discard any seeds. Set aside.
Preheat the oven to 350°F and position a rack in the middle.
Line an 8-inch round cake pan with parchment paper: Place the pan on top of a piece of parchment paper, and trace the bottom of the pan to create a circle pattern. Cut out the circle and place it inside the bottom of the cake pan. Cut out two 8 x 2-inch strips of parchment paper and place them along the inner wall of the pan.
Place the pistachios in the bowl of a food processor. Pulse until the nuts are pulverized and resemble a coarse flour. Add the boiled mandarins, the honey, eggs, coconut flour, baking soda, and baking powder. Process until the batter is smooth. Pour the batter into the prepared cake pan.
Bake until the cake is golden brown on the top and a toothpick inserted into the center of the cake comes out clean, 20 to 30 minutes. Let cool for 10 to 15 minutes, and then invertit onto a cake stand or platter. Remove the parchment paper and serve. To store, let the cake cool to room temperature,wrap it in plastic wrap or a beeswax cloth, and refrigerate it. The cake will keep well wrapped in the refrigerator for up to 5 days.