I thought I had seen that effect before, so I checked my collection of old specimens.
To my delight, I quickly found two specimens that are worth showing. Both of them are "June beetles", members of the scarab family that THIS reference says is closely related to the stag beetles.
This first one is particularly nice, though it may take a little study to recognize why.
This image is a crossed eye stereo pair. If you can see stereo, it may gradually become apparent to you that several of the large golden hairs in the upper part are actually "copies" of other hairs in that same area, reflected from the mirrorlike surface of the eye.

This seemed a little too extreme to be true, but I confirmed by direct manipulation under a stereo scope that those really are reflections. Move one hair with a pin, and its partner that appears below the surface moves in just the same way, nudged by a reflection of the pin. It's quite unexpected. The reflection of the geometrically straight pin, not shown here, indicates that surface is slightly dimpled, presumably with one dimple for each ommatidium.
By the way, the golden reticulated pattern is caused by separation of internal tissues when the specimen dries. In live beetles and fresh specimens, the eye is almost black.
I do not know exactly what species this is. I find the adults occasionally in summer, on a sidewalk near a lighted wall at a local building. Here is a picture of the beast:

The other specimen is a classic Ten-Lined June Beetle, collected some 28 years ago, that I used for my first experiment with telecentric lenses, 15 years ago. It can be seen in overview HERE.
The following is not a stereo pair. I mention this because I have accidentally tried several times to fuse it up. That actually works, but because the views are identical except for lighting, the stereo geometry looks flat.
The point of this pair is structure revealed by the lighting. On the left, with a strong specular reflection from the surface, you can see that the surface is slightly dimpled. But on the right, with very diffuse lighting so the surface does not show, you can see that the same area of the eye has shows the ommatidia structure strongly revealed in some of the golden bands.

The following is a stereo pair. The interesting thing here is that there's a clear separation between the smooth but dirty surface, and the hexagonal grid of ommatidia bolow it.

I hope you find this as interesting as I do.

--Rik
Technical: Closeups with 10X Mitutoyo stacked at 0.005 mm, cropped to show what I wanted. Diffuse illumination by electronic flash far back from a 3" diameter hemispherical diffuser; hard illumination for surface reflections using a single Jansjo lamp placed directly against the same diffuser. Synthetic stereo at +- 6 degrees.