Variation: Substitute one medium ham steak, cut into cubes, for the ham hocks. Or use both if you like lots of ham.
Pre-prep:
On the night before cooking, sort beans, removing any that are broken or discolored. Rinse remaining beans, then place in a large bowl and cover with hot tap water. Add about 1 tablespoon baking soda and stir. Let stand for an hour or two, until water is cooled off. Cover and refrigerate overnight.
Preparation:
Rinse ham hocks, removing any loose bone fragments. Place in large pot or crock pot. Drain beans from baking soda mixture and rinse thoroughly. Toss beans with onion, celery, and carrots, then add to pot. Add garlic, Bay leaves, dry mustard, and pepper. Add half & half, chicken broth, and enough water to cover the beans.
For stovetop, cook covered on medium-high heat for 2-3 hours. For crock pot, cook on low for 12-14 hours
Near end of cooking time, remove ham hocks and let cool on cutting board. Trim the meat from the bones and add it back into the beans. Add salt to taste. Serve with cornbread.