Preheat the oven to 350 degrees F (175 degrees C).

Prepare the cookie crust: Stir together flour and brown sugar in a medium bowl. Rub in butter using your hands or a pastry blender. Press into an ungreased 9-inch square pan.

Bake in the preheated oven until lightly browned at the edges, about 15 minutes. Set aside.

Make the cookie filling: Beat eggs in a medium bowl until light. Mix together brown sugar, flour, baking powder, and salt; stir into eggs. Mix in coconut, walnuts, and cherries; spread the batter evenly over the baked crust.

Return to the oven and bake until brown, about 25 minutes. Set aside to cool.

Make the frosting: Mix confectioners’ sugar, butter, water, and vanilla in a small bowl until smooth. Add more liquid if necessary to make a more spreadable mixture. Spread over cooled bars before cutting into squares.