Pour your dry beans onto a clean baking sheet. Sort through them carefully to pick out any tiny pebbles, dirt clods, or shriveled beans before rinsing them under cold water.
Layer the rinsed Great Northern beans, chopped carrots, and chopped celery at the bottom of your slow cooker. Pro Tip: Do not add a single grain of salt at this stage. Introducing salt too early in a long bean simmer chemically toughens the outer skins, which causes them to take twice as long to soften.
Lay the heavy smoked ham hocks directly over the bean and veggie base, pushing them down gently so they are nestled flat.
Pour the 6 cups of water (or low-sodium stock) directly into the pot, ensuring the hocks are mostly submerged. Dust the black pepper, cayenne pepper, and slip the bay leaves down the inside walls of the crockpot.
Secure the lid tightly and cook on Low for 6 to 8 hours (or High for 4 to 5 hours). The steady, low temperature gently draws the smoky fats and rich collagen out of the hocks, transforming the plain water into a deeply savory, gelatinous broth.
Once the beans are completely tender, carefully fish out the hot ham hocks. Let them sit on a board for 5 minutes, then strip away the pull-apart meat. Shred it into bite-sized pieces, discard the bones/connective tissues, and slide the meat back into the pot.
Before serving, take a heavy wooden spoon or potato masher and crush a half-cup of the cooked beans directly against the inside wall of the slow cooker. Stir it thoroughly. The exposed starches will immediately cream into the broth, thickening it into a rich pot liquor. Season generously with salt now, tasting after each pinch until it perfectly counters the smoky meat.