Works by hooking up with wireless bluetooth phones of course - you knew that!
I'm really posting my idea of how to mould it.
Here's my idea - it's a technique I've seen used by a guy when making models to make irregular-shaped parts fit in an exact matching hole.
Gonna be difficult to imagine what I'm trying to explain, but I'll try anyway.
Firstly, I would cut the hole as close as you can to the shape of the unit. To get a clean hole and make it fit as close as possible to the shape of the BT unit around the button area, wrap a few layers of reflective insulation tape around the sides of the buttons. Use a sharp scalpel from an art shop to cut it down - don't tear the tape off or use scissors as you need to keep the surface of the taped area as smooth as possible. Do this neatly and make sure you use a few layers so that you give yourself enough of a small gap between the hole and the buttons, so you don't have to wedge it in afterwards. This will depend on how thick the tape is of course.
Next step, you need to attach the front panel of the BT unit to the hole using whichever method (hot glue, etc). At this point, make sure the front of the BT unit and the surface you're attaching it to are completely flush.
Next bring up the buttons from behind the front panel of the BT unit and attach it back. Might be worth masking off the tops of the buttons too so you don't destroy them with filler.
At this point you can start applying filler to the gaps, including around the buttons (which are masked off, of course). Make sure the filler sits slightly proud of the surface.
Once the filler has set, carefully prise the buttons away, and you should end up with two holes with exactly moulded contours to match your buttons.
Use a sanding block to rub down the excess filler - a sanding block will ensure the entire surface is flat.
The only problem i see with this method is that the Parrott has a bevelled edge, so it might look strange having bevelled buttons on a flat surface.
Or, you could mask off the whole thing and mould a hole so that the entire unit fits flush to panel - that way, at least you can remove it if you want to sell the car.
Hope it helps anyway.