Begin by rinsing split peas under cold water, removing any debris. Finely chop onion, carrots, celery, and mince garlic.

In a large pot, heat olive oil over medium heat. Add onion, carrots, celery, and garlic, sautéing until softened and fragrant, about 5-7 minutes.

Add rinsed split peas, broth, and bay leaves. If using, include smoked turkey legs or ham shank. Bring to a gentle boil, then reduce to a simmer.

Let the soup simmer uncovered for 30-40 minutes, stirring occasionally. The split peas will soften and thicken the soup.

For a creamier texture, use an immersion blender to puree part of the soup. Adjust thickness with broth or water as needed.

Remove bay leaves and adjust seasoning with salt and pepper. Serve warm, garnished with fresh herbs or alongside crusty bread.