Sauté sausages in heavy large pot over medium-high heat until fat begins to render, about 4 minutes. Add potato, onion, and rosemary. Sauté until onion is soften, about 5 minutes. Mix in split peas, then broth. Bring soup to simmer. Reduce heat to low. Cover and simmer until peas are tender, stirring occasionally, about 50 minutes. If desired, thin soup with water by 1/4 cupfuls. Season soup to taste with salt and pepper. Ladle into bowls and serve.