Preheat the air fryer to 300℉.
Place the blended cottage cheese, flour, baking powder, and sea salt in a large bowl. Using a silicon or wooden spoon, stir until combined. Then, using your hands, press together until a ball has formed.
Transfer the dough to a floured work surface. Knead together until smooth. You may need to sprinkle more flour over the top, so it is not super sticky.
Divide the dough into 4 equal pieces. Roll into a log about 6 inches long. Cut each log into 5 pieces. Roll each piece into a ball. Set aside.
Place the brown sugar and cinnamon into a small bowl and whisk to combine.
Roll each ball in the melted butter, then transfer to the cinnamon sugar and roll in the cinnamon sugar. Set aside.
Line the air fryer with parchment paper. We recommend using a round parchment paper insert. If you do not have one, you may need to layer two pieces of paper to make a bowl shape. Place all of the balls into the insert. They will be touching.
Air fry for 20 to 25 minutes. There will be a little bit of liquid on the bottom when they are done. It is the brown sugar melting.
Make the frosting: While the monkey bread is cooking, add all the ingredients to a bowl and use an electric mixer to mix the ingredients together. Be sure the cream cheese is softened, or you will end up with lumpy frosting.
Rest for 10 minutes before serving with the frosting. You can pour the frosting over the monkey bread or use it as a dip.