Because all these vegetables will be boiling in soup for two hours, it's not necessary to obsess over the exact size and shape of each vegetable. However, it's ideal to cut everything to approximately the same size. Your soup will look amazing and the ingredients will have the perfect textures.
Cut the green cabbage (1 lb) open. Cut the hard core away and discard it. Cut the cabbage into thick strips, then into bite-sized pieces.
Trim and discard the dirty ends of the celery (3 stalk). Break the stalks by hand to see the tough, stringy fibers along the outer, greener surface of celery stalks. They can be difficult to eat and digest, so pull off any stringy fibers that stick out. Then, dice the celery into small, bite-sized chunks.
Peel the potatoes (2 ) and carrots (2 ) if you like. You'll also be dicing these. For the potato, wet your knife to prevent sticking, then cut the potatoes in halves, then quarters, then into large cubes. Cut the thickest ends of carrots in half lengthwise, then into bite-sized chunks. (If you have skinny carrots, you might not need to halve them.)
Cut the red onion (1 ) open so you can stabilize it on its cut, flat base. Then cut across once to halve again, and dice into chunks.
Cut the chili pepper (0.50 ) open. Discard the seeds and core to reduce the spice level, or include them (or add more chili pepper!) for more of a kick. Chop the pepper into small pieces.
Cut the tomatoes (3 ) in half, then into quarters, then into large bite-sized pieces. Dice the last tomato (1 ) into smaller pieces. The large chunks provide texture, and the smaller pieces will melt into the broth for more flavor.
Smash the ginger (2 oz) and roughly cut it into small pieces. Smash the garlic (3 clove). To make it easier to fish out when eating, leave these aromatics in smashed chunks.
Cut the lemon (0.50 ) in half.