Fry over medium heat in the pressure cooker until it starts to turn golden.
Lay the beef neck flat in the base of the pressure cooker and add stock until it is just covered. Reserve the rest of the stock.
While stock is heating, rinse and quarter the potatoes (leave the skin on) and add to the pressure cooker.
Peel the carrot and cut in coins about 1/3 inch thick. If you carrot is exceptionally fat, cut the larger coins in half down their diameter. Add carrots to the pressure cooker.
Add the barley to the pressure cooker, then add more stock to until meat and veggies are just covered. Reserve the remaining stock.
Secure the pressure cooker lid and bring to temperature over high heat.
Turn heat down until it just maintains pressure and cook for 1 hour. Turn off heat and allow 15 minutes of natural release.
While meat, potatoes, carrots, onion, and barley are cooking, dice the tomatoes, mushrooms, zucchini, and celery into 1/2 inch cubes. Remove the stems from the spinach.
After the 15 minutes of natural release, if still pressurized, run the whole pressure cooker under tap water to cool.
When cooker loses pressure, open and remove the beef neck. Use a fork to take the meat off the bone, discard the bone and return the meat to the pot.
Add the tomatoes, mushrooms, zucchini and celery. Add more stock if required to just cover the veggies, but it's not likely that this will be necessary now that the bone is gone.
Simmer with the lid off until zucchini is almost fork-tender (10 to 15 minutes, depending on how small the zucchini ended up). Then add the spinach and continue cooking until zucchini is fork-tender but not mushy.
Serve immediately with whole-grain bread for dipping.