Prepare Ingredients: Rinse and sort split peas. Dice ham and vegetables.
Sauté Aromatics: In a large pot or Dutch oven, sauté onions, carrots, celery, and garlic over medium heat until softened, about 5 minutes.
Add Peas and Liquid: Stir in split peas, broth, water, bay leaf, and thyme. Add diced ham or ham bone.
Simmer: Bring to a boil, then reduce heat and simmer, uncovered, for 60–75 minutes, stirring occasionally, until peas are soft and soup has thickened.
Adjust Seasoning: Remove bay leaf and ham bone (if used). Taste and season with salt and pepper.
Serve: Garnish with fresh parsley or croutons if desired. Serve hot with crusty bread.