In a large saucepan, heat the olive oil over medium heat. Add the sausage and cook, stirring occasionally, until browned, about 5 minutes. Transfer to a bowl.
Return the pan to the heat, add the onion, carrots and half the garlic and cook, stirring occasionally, until softened, about 5 minutes. Add the split peas, chicken broth, and 1/2 teaspoon each salt and pepper. Cover and bring to a boil, then lower the heat and simmer, covered, until the peas begin to break down, about 50 minutes.
Using a blender, puree the soup. Return to the saucepan and heat through over medium heat. Stir in the reserved sausage.
In a small bowl, combine three-quarters of the lemon peel with 1/2 cup mint and the remaining garlic. Stir into the soup; season with salt. Ladle into bowls and top each portion with the remaining lemon peel and mint.