1. Bring 3 quarts water, ham and bay leaves to boil. Cover and reduce heat to low and simmer until meat is tender and pulls away from the bone, approx 2 – 2 ¾ hours.

2. Take ham out of water and set aside on a plate to cool. (To reduce fat, you can refrigerate the liquid and let the fat harden – then just scrape off and reheat liquid.) Add split peas and thyme to water and simmer until peas are tender but not dissolved, about 45 minutes. Cut up potatoes and add them in halfway through.

3. Meanwhile, when ham is cool enough, shred meat and set aside. Give rind and bone to the dogs.
While peas are simmering, heat oil or butter in large skillet over high heat until shimmering. Add onions. Saute until soft. Add carrots and celery. Saute, stirring frequently, until most of the liquid evaporates and vegetables begin to brown, 5-6 minutes. Reduce heat to medium-low. Add butter, garlic, and sugar. Cook vegetables, stirring frequently, until deeply browned, 30-35 minutes or until cooked but carrots still have a bite to them; set aside.

4. Add shredded ham to soup; simmer until potatoes are tender and peas dissolve and thicken soup; about 20 minutes more. Add vegetables. Season with ground black pepper.

The finished soup will thicken as it stands but can be thinned with water when reheated.