This is one of my favorite soups and makes just the right amount in my 2-quart slow cooker. So good you won't even miss the ham. I've been making this recipe for about 40 years and it comes out great every time.
Place the split peas in a mesh colander and rinse well, picking out any debris.
Add the potato, onions, garlic, celery seed, salt, and pepper into the insert of a 2-quart slow cooker or crockpot.
Add the chicken broth, water, and split peas.
Cover and cook on low for 5 hours, uncover, stir, and add the frozen carrots, recover and continue cooking for 1 more hour.
Notes
Don't be tempted to add tomatoes to the recipe, acidic ingredients will keep the split peas from softening.
Saute onions, garlic, carrots, and celery in a pan with a bit of olive oil before adding them to the slow cooker. This enhances their flavor and helps them hold up better during the long cooking time.
If you're not vegetarian or vegan, these ingredients can add a lot of depth and smoky flavor to your split pea soup. If you are using one of these, place it in the slow cooker first, then add the peas and vegetables.
Once all the other ingredients are in the slow cooker, add your broth or water. The liquid should just cover the ingredients. You can always add more later if needed.
Cook your soup on the low setting of your slow cooker if possible. This allows the flavors to meld together more fully and ensures that the peas get really soft and creamy.
Wait until the end of cooking to adjust the seasoning of your soup. The flavors will concentrate during cooking, and if you add salt in the beginning, your soup could end up too salty.
If you like your split pea soup very smooth, you can remove about half the soup and blend it in a blender or with an immersion blender, then stir it back in. If you prefer it chunkier, you can skip this step.
I like a thick pea soup, but if you want a thinner soup, add extra liquid during cooking.
Old split peas will not be softened properly. For best results, pay attention to the best buy date on the package.