Dice the potatoes into small cubes. Finely chop the onion and grate the carrot. Slice the sausages into rounds or strips.
In a pot, bring water or broth to a boil. Add the diced potatoes, season with salt, and simmer on medium heat for 10-12 minutes.
In a frying pan, heat the olive oil. Sautéthe onion and carrot until softened (about 5 minutes). Add the sausages and cook for another 2-3minutes.
Transfer the sautéed vegetables and sausages into the pot with the potatoes.
Cut the melted cheese into small pieces and stir it into the soup. Continue stirring until the cheese is fully melted, creating a creamy consistency.
Taste the soup and adjust the seasoning with salt and pepper if needed. Serve in bowls, garnished with fresh herbs.