Rinse the great northern beans thoroughly under cold water and sort through them carefully to remove any stones or debris. Dice the onion into bite-sized pieces, dice the carrots into uniform 1/2-inch pieces (this ensures even cooking throughout the slow cooker), chop the celery stalks into 1/2-inch pieces, and mince the garlic cloves. Having everything prepped and ready before adding to the slow cooker ensures even flavor distribution and cooking.
Add the rinsed beans, ham bone, and all diced vegetables (onion, carrots, celery) and minced garlic to the slow cooker. Pour in the chicken broth and add the bay leaves, parsley, thyme, celery salt, and dry mustard. Stir everything together to distribute the seasonings evenly. I like using Colman's dry mustard because it adds a subtle depth without overpowering the soup—it complements the ham beautifully without being obvious.
Cover the slow cooker and cook on low heat for 7-9 hours. The long, gentle cooking allows the beans to become creamy and tender while the ham bone releases its deep, savory flavor into the broth. The aromatics will soften and meld with the liquid, creating a rich base for the soup.
Carefully remove the ham bone from the slow cooker using tongs and set it aside to cool slightly. Once cool enough to handle, shred any meat clinging to the bone and discard the bone, fat, and any cartilage. You'll be adding the pre-cooked ham cubes separately, but this step captures any additional meat flavor from the bone.
Using an immersion blender, carefully blend about one-third to one-half of the soup while it's still in the slow cooker, making sure to blend around the ham bone area to catch the starches from the beans. This creates a naturally creamy texture without adding cream or thickening agents—the broken-down beans thicken and enrich the broth. Leave plenty of whole beans and vegetables for texture.
Stir the 2 cups of diced ham cubes into the soup along with a few dashes of hot pepper sauce and black pepper to taste. Let the soup heat through for 2-3 minutes on low to warm the ham and allow the pepper sauce to distribute evenly. Taste and adjust seasonings as needed—I find the hot sauce adds just the right amount of brightness to cut through the richness of the ham and beans.
Ladle the soup into bowls and serve hot. Remove the bay leaves if they're visible. The soup is hearty, warming, and deeply flavorful with tender beans, shredded ham, and vegetables in a rich, creamy broth.