First prepare the gnocchi (if making own) - peel and cut the potatoes into chunks then place in a pan with plenty water. Bring to a boil then reduce heat to a low boil. Cook for around 7-10min until the potatoes are tender to a knifepoint. Drain, mash (or put through a ricer) and set aside until cool enough so easy to handle.
Meanwhile, you can start the lobster sauce - toast/dry fry the lobster shell over a medium heat in a dry skillet/frying pan. Turn after a couple minutes and again as far as possible. You'll start to see the shell dry a little. While the shells are toasting, dice the onion and carrot relatively small.
Carefully add the water to the pan with the lobster shell, gradually at first to avoid it splashing too much. Add the onion, carrot and thyme, cover and bring to a boil. Reduce to a simmer and cook for around 10-15minutes until the carrots are just tender.
While the sauce is simmering, make up the gnocchi by adding the flour, egg and goat's cheese to the cooled mashed potatoes and mixing until well combined. You might need to finish it off by hand.
Turn the dough out onto a floured surface, break off chunks at a time and roll the mixture into logs. Cut chunks from the log that are small bite-sized pieces, roll gently in your hands to form a ball then set aside on a floured surface. Repeat with all of the mixture.
Once the carrots are tender, remove the lobster shells from the pan and blend the stock-vegetable mixture that remains (either use a stick/hand blender or transfer to a blender). Add the cream to the mixture and simmer gently for a few minutes until it thickens slightly. Add the cornstarch/cornflour and mix in to help. Add the parmesan and the lobster broken in to relatively small pieces and stir to mix through. Cook for a minute or two more then set aside.
To cook the gnocchi - bring a shallow pan of water to a boil over a relatively high heat then cook the gnocchi in batches so you don't overcrowd the pan. Make sure the water stays boiling as you cook. The gnocchi will float to the surface once they are ready. If they don't do this after a minute or two, nudge them with a spoon as they may have stuck to the bottom of the pan.
Remove the cooked gnocchi from the pan with a slotted spoon and add them to the lobster sauce.
Note - if you think there are too many gnocchi for the number of people/amount of sauce then freeze some before cooking - lay on a baking sheet/tray in a single layer, not touching, and freeze then transfer to a freezer bag. Cook from frozen in same way as usual, they'll just take a minute or two more to cook.