Place the rinsed split peas, diced ham, sliced carrots, diced onion, chicken broth, smoked paprika, minced garlic, and bay leaf into the slow cooker.
Stir the ingredients together until the smoked paprika is evenly distributed.
Cover the slow cooker and cook on low for 8 hours.
Remove the bay leaf after cooking. Stir the soup to help the split peas finish breaking down into a thicker consistency.
Taste and add salt and pepper as needed before serving.