Chop carrots and onion.  Heat butter over medium heat, in a large pot; add chopped carrots, onions and peas. Cook until onion is translucent and beginning to caramelize; carrots will be soft as well.

Sprinkle the flour over the vegetables, stirring, allow vegetables to mix with flour; cook for about 10 minutes; flour will darken in color.

Slowly add stock, whisking at same time, to keep from turning lumpy. Turn heat up to begin boiling; once boiling, turn heat back down to simmer for 20 minutes.

Once all vegetables are soft, remove from heat and allow to cool enough to puree; add parsley and salt and pepper to taste, and puree.

Pour puree back into a large pot, add milk and cream, simmer again. If too thick, more stock may be added.  Chop green onions and top soup with them.