Add soft tofu, yogurt and cottage cheese to a fine mesh sieve or colander lined with cheesecloth. Top with paper towel or cheese cloth and weigh this down with a light weight, such as a small can.
Strain overnight, or at least 6 hours.
For the cake
Preheat the oven to 375F and spray a 12 x 18 baking sheet with cooking spray, then line with parchment paper. (The cooking spray will help the parchment paper adhere to the baking sheet, which is really important, so you don’t want to skip this step. If you don’t have cooking spray, brush very lightly with oil.)
Using a stand or electric mixer, beat the eggs and egg whites until very foamy, about 10 minutes.
Meanwhile, add the almond meal, coconut and oat flour, matcha green tea powder and salt to your food processor and process until well combined.
Transfer to a large mixing bowl and add applesauce, buttermilk and vanilla extract. Mix delicately with a rubber spatula until very well combined. Set aside.
Bring honey to a boil and slowly pour it into the egg mixture, without stopping the mixer. The best way to do this is to pour the honey as close as possible to the side of the bowl, so that it doesn’t come in contact with the beater.
Continue whisking the eggs for another 3-4 minutes
Using a rubber spatula, delicately fold in this egg mixture into the previously reserved batter and mix until well incorporated. Very gingerly fold in the black beans.
Spread that cake batter as evenly as possible onto the prepared baking sheet and cook in a 375F oven for about 25 minutes, or until top is nice and golden brown.
Take out of the oven and allow to cool for 2-3 minutes, then flip sheet cake over a clean tea towel. Do not remove parchment paper at this point. Allow to cool completely.
For the icing
Add strained tofu, cottage cheese and yogurt to your food processor and process until smooth and creamy, about 2 minutes.
Pop coconut butter in the microwave for a few seconds just to soften it a little bit.
Add it to the cheese mixture, along with honey, matcha powder, whey protein powder, and coconut flour and process again for about a minute.
Transfer the icing to the refrigerator to firm up for at least 20-30 minutes
Assembly
Remove the parchment paper from the cake sheet and cut out the edges, then cut the sheet into three equal rectangles.
Lay one of the rectangles on a cake board or plate and spread about one third of the icing evenly over its entire surface. Make sure you go all the way to the edge.
Top with a second cake rectangle and spread another third of the icing. Repeat with the last layer of cake.
Sprinkle unsweetened shredded coconut over the cake.