Prepare Ingredients: Chop onions, carrots, and celery. Rinse split peas under cold water to remove debris. If using a ham bone, trim excess fat.
Sauté Aromatics: Heat butter or oil in a large pot over medium heat. Add onions, carrots, and celery, cooking until softened (5-7 minutes). Stir in garlic and cook for 1 more minute.
Simmer the Soup: Add split peas, ham bone, bay leaf, thyme, chicken stock, and water. Bring to a boil, then reduce heat and simmer uncovered for 60-90 minutes, stirring occasionally.
Adjust Texture: If soup is too thick, add more broth. If you prefer a smoother soup, blend a portion and mix it back in. Remove ham bone, shred any remaining meat, and return it to the pot.
Final Touch: Stir in diced ham during the last 15 minutes to warm it through. Adjust seasoning with salt and pepper as needed.
Serve & Enjoy: Remove bay leaf before serving. Ladle into bowls and top with croutons, bacon bits, or a swirl of cream.