Melt butter in soup pot. Add onions and carrots and cook over low heat covered until vegetables are tender and lightly colored about 25 minutes.
Add parsley, stock, and potatoes, and bring to boil. Reduce heat, cover and simmer until potatoes are very tender, about 30 minutes.
Add dill, remove soup from heat, and let it stand covered for 5 minutes.
Pour soup through a strainer and transfer the solids to the bowl of a food processor fitted with a steel blade. Add 1 cup of the stock and process until smooth.
Return pureed soup to the pot and add additional cooking liquid (about 3-4 cups) until the soup reaches the desired consistency.
Set over low heat, and add salt and pepper, and gradually stir in the grated cheese. When all the cheese is melted, serve immediately. Garnish with croutons.