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Begin by placing the rinsed split peas, diced onion, carrots, celery, and minced garlic into the bottom of the slow cooker.
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Nestled the ham bone, ham hocks, or diced ham into the center of the vegetables and peas. Pour in the broth and water, then add the dried thyme and the bay leaf.
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Cover the slow cooker and cook on low for 7 to 8 hours or on high for 4 to 5 hours.
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The soup is ready when the peas have completely softened and broken down, creating a naturally thick and creamy consistency.
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Once the cooking time is finished, carefully remove the ham bone or hocks from the slow cooker.
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Trim any meat off the bone, shred it into bite-sized pieces, and return the meat to the soup while discarding the bone and any excess fat. Remove and discard the bay leaf.
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Give the soup a vigorous stir to help the peas incorporate into a smooth base. If you prefer a completely smooth texture, you can use an immersion blender to blend a portion of the soup.
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Taste the soup before adding salt, as the ham and broth often provide plenty of saltiness on their own, then finish with a generous pinch of black pepper. Serve hot with toasted bread or croutons.