Normally hidden on the back side of the joint, but if executed well it can make a nice feature for a display surface.
Prepare a simple mitre as normal
As shown, the grain should run the length of the butterfly for maximum strength
Clean up all the edges, so that they are square to the face, straight and smooth. This will allow for easier fitting and best adhesion
Position the butterfly over the mitre joint, without it being too close to any edge
Holding the butterfly absolutely still, knife it's outline onto the joint
Here I've penciled in the knife line for clarity
Excavate a knife wall within the area to be removed...
...and remove the central waste close to the thickness of the butterfly
The base of the excavation has to be level for a good glue joint, and a router plane makes this task easier
Make sure all the corners are cleaned out thoroughly, so that the key will fit without any problems
Test fit the key, without pushing it fully home just yet, and make any necessary alterations
Now it's time for glue, which should be spread evenly over the bottom...
...and sides of the hole
The key can now be inserted, and pressed or hammered in to full depth
Clamp until cured...
...before flushing the surface with a plane
Now watch the video: