It'll have a routed lip on one side, silicone adhesive, then use a bead of wicker reeding on the other side. I can pre-shape the reeding to fit right in the 4" circle, then use a thin bead of silicone to make it stay.
I was going to suggest that you cut half way through with a hole-saw (Like an attachment to a hand drill) Then cut from the other side with a slightly smaller hole saw, maybe a
1/4" smaller. I'd think that the plug should be knocked out fairly easily (But it should be noted that I'm often wrong).That would leave a 1/8" stop. Then add your bead of wicker to hold the glass in place.