Toothed plastic cup on bottom bracket got sheared off - still removable?
From the look of it, the drive side teeth may yet offer some hope.

The first thing I would do is get some penetrating oil in the threads to maximize your chances of being successful before the teeth get destroyed completely. Apply it around the outside and see if you can get it to weep in, and you can use your BB cable guide's mounting screw hole to apply it from the inside. I use Finish Line Chill Zone and I'm very liberal with it and I recommend this approach as the cold shocking and thermal contraction/expansion seems to do a lot to break up corrosion and get oil worked in. Let it soak 24 hours and then clean and de-grease the outside where the tool will be engaging.

It's not clear whether you're dealing with corrosion here. If you're confident you're not you can skip that step, but it does look to me like the drive side teeth are offering you one more go, whereas doing this once all the teeth are completely gone is one of the more truly difficult things I've come across working on bikes, so making the most of any remaining attempts would be wise.

You need to rig up a way of holding the tool on to the splines tightly. If the spindle is hollow, you can use a quick-release skewer for this, and potentially some washers depending on what kind of tool you're using. Otherwise get a suitably long M8x1 bolt and some washers. Get the tool as lodged into the splines as you can. Tap it in with a hammer or use the quick-release/bolt setup. Then use a long adjustable wrench on the tools's wrench flats. Make sure you're going the right direction, clockwise to loosen the drive side for most bikes.

If that doesn't work, you're probably looking at needing to smash or ram the cartridge through the plastic cups or something similar.