Rinse 1 pound dried split peas and sort out any debris
Heat 1 to 2 tablespoons oil or butter in a large pot over medium heat
Add 1 chopped onion, 2 chopped carrots, and 2 chopped celery stalks
Cook until softened, about 5 minutes
Add 2 minced garlic cloves and cook for 1 minute
Add the split peas, 8 cups water or broth, 1 bay leaf, 1 teaspoon salt, and 1/2 teaspoon black pepper
Add 1 ham bone, ham hock, or diced ham if desired
Bring to a boil
Reduce heat to low and simmer, covered, for 60 to 90 minutes
Stir occasionally and add more water if needed
Remove the bay leaf and ham bone or ham hock
Shred any meat from the bone and return it to the pot if using
Adjust seasoning with more salt and pepper
Serve hot