Soak 1 (16 ounce) package green split peas in 4 quart (or larger) Dutch oven overnight. Next day, drain. Add fresh water, about 5 cups. Bring to boil, slowly, skimming foam as it forms. Add 2 bay leaves.
Gently cook until peas start to disintegrate, about 1 1/2 hours. Add 1/2 teaspoon salt and 1/4 teaspoon pepper. Add ham bone with attached meat from previous dinner (1/2 ham, baked). Add 5 to 6 carrots, shaved and cut into 1/2 inch rounds. Cook until almost tender.
Add 6 to 7 peeled whole onions, small to medium size. Cook until tender. Remove ham bone to platter. Cool. Remove bay leaves. Adjust seasoning to taste. When ham bone has cooled, cut off ham meat and cut into bite-size pieces. Add to soup.