Bring the broth to a boil in a sufficiently large saucepan. Add the peas, carrot slices and potato pieces and cook until the vegetables are cooked (about 30 minutes). Add salt and sugar to taste.
Remove some of the soup and puree to a pulp with the hand blender. Add this to the soup again (makes it a bit thicker and more intense in taste). Season again to taste.
Set the stove to low, stir in the parsley and add the sausages to the saucepan to warm up. Instead of the sausages, you can also use normal meat sausages or do without the meat insert altogether. If children eat with you, small cocktail sausages are also ideal.