Empty the 2 pounds of dried Great Northern beans onto a clean baking sheet or counter. Pick through them carefully to discard any small pebbles or damaged beans, then transfer them to a colander and rinse thoroughly under cool running water.

Place the rinsed, dry beans directly into the ceramic basin of your slow cooker.

Add the finely chopped carrot and celery straight into the pot with the beans to establish a sweet, aromatic flavor baseline.

Nestle the 1 ½ pounds of ham hocks firmly down into the bean layer so they are centrally positioned.

Pour the 6 cups of water or chicken broth evenly over the ingredients, ensuring the liquid fully covers the beans and partially submerges the pork.

Add the black pepper and cayenne pepper, stirring the surrounding liquid gently to distribute the spices without disturbing the nestled ham hocks. Do not add salt yet, as cooking dried beans in highly salted water from the start can tighten their outer skin membranes and prevent them from softening properly.

Secure the slow cooker lid tightly. Cook on Low for 6 to 8 hours (or on High for 4 to 5 hours) undisturbed. Avoid lifting the lid during the first few hours, as escaping steam will significantly lower the cooking temperature and extend your wait time.

Around the 5-hour mark, check the beans for doneness; they are finished when they are completely plump, tender, and creamy to the core.

Carefully lift the hot ham hocks out of the slow cooker and transfer them to a cutting board. Use two forks to shred the tender, smoky meat away from the bone and skin, discarding the fat and bone fragments.

Slide the shredded pork meat straight back into the bubbling bean matrix. Taste the rich broth and season with salt to your personal preference. Stir firmly for 60 seconds, allowing the starches from a few slightly crushed beans to naturally thicken the liquid into a silky gravy before serving hot with a side of cornbread.