What's the best way to hang this large picture on insulated plasterboard?
I'd use picture wire between the two D-rings to hang the picture. Leave some slack in the wire, as that will give you some scope for adjustment to make sure it can hang level.

Usually, I'd suggest picture hooks, but with insulation in front of the plasterboard, my suggestion would be to drive decent length screws into the studs, leaving the head protruding a little, and hang the picture wire over the screw heads