Whisk together flour, cocoa, baking powder, baking soda and salt.
Using a stand mixer beat butter and brown sugar together until creamy, 2 minutes.
Add egg and then alternately add flour mixture and Chobani starting and ending with flour mixture.
Scoop ¼ cup mounds of batter onto two parchment paper-lined baking sheets and bake on the upper-middle and lower-middle racks at 350°F until puffed and springy to the touch, about 15 minutes, rotating the pans midway through baking. Set aside to cool 10 minutes then transfer to a wire rack to cool completely.
Add yogurt to bowl of a stand mixer and sift confectioners’ sugar over it. Beat to combine, then add cream cheese and beat until smooth.
Spread 1 T of filling onto flat part of half the cakes. Top each with another cake and serve.