No, you cannot grow Brussels sprouts from store bought produce in any useful way. Those little green heads are immature buds that lack the parts needed to become new plants. Unlike some vegetables, sprouts will not root or sprout into something you can grow.
I tried this after reading about starting vegetables from scraps online. The sprouts sat in water and soil for weeks. No roots appeared and no new growth happened at all. They just rotted away despite my best efforts. Save yourself the trouble and skip this experiment.
The problem comes down to plant biology. Brussels sprouts are axillary buds that grow along the main stalk of the plant. They have no root cells or stem cells that could grow into a new plant. This makes them different from lettuce cores or green onion bases.
Propagating Brussels sprouts requires seeds from a mature plant that has flowered. Brussels sprouts are biennials. They grow leaves and sprouts the first year and produce flowers and seeds in their second year. Most gardeners harvest before this happens.
Vegetables you can regrow from scraps include green onions, celery, romaine lettuce, and bok choy. These work because their base sections contain growing points. Those growing points can make new leaves and roots. Brussels sprouts lack this ability.
The best way to get new Brussels sprout plants is buying seeds or transplants from a garden center near you. Seeds cost just a few dollars for a packet that grows dozens of plants. Transplants run about 2-4 dollars each and save you the seed starting step.
Start seeds indoors about 4-6 weeks before you plan to transplant outside. Use seed starting mix in small pots or cell trays. Keep the soil moist and warm until seedlings appear in about a week. Then move them to bright light near a sunny window.
You can save seeds from your own plants if you let one overwinter and flower the next spring. This takes planning since you need to protect the plant through cold winter months. Most home gardeners find buying fresh seeds each year easier than saving their own from mature plants.
Skip the kitchen scrap experiment and buy proper seeds or starts from a garden center instead. You will save time and get healthy plants that produce real harvests for you. The few dollars spent on seeds pays off in pounds of fresh sprouts come fall.
Read the full article: Growing Brussels Sprouts: Professional Tips for Larger Harvests