You do that by using Boolean operations. It is available in Body selection mode.
To create the negative one, you select the first object (the panel) and choose the option "Boolean *test*"->"Difference" and then pick the second one (the wings).
To avoid to get problems (error) I recommend you to slice the panel a couple of time. It doesn't needs to be much. You can use try and error (just redoing the boolean operation) to get the idea about the good amount of slices. If you don't care about the poly count, then you can do a lot and be happy.
Also, the faces cannot be coplanar. So, for your requirement you need the wings to be "higher" than the panel in order it be cut.
To create the negative one, you select the first object (the panel) and choose the option "Boolean *test*"->"Difference" and then pick the second one (the wings).
To avoid to get problems (error) I recommend you to slice the panel a couple of time. It doesn't needs to be much. You can use try and error (just redoing the boolean operation) to get the idea about the good amount of slices. If you don't care about the poly count, then you can do a lot and be happy.
Also, the faces cannot be coplanar. So, for your requirement you need the wings to be "higher" than the panel in order it be cut.