If using fresh broccoli, rinse and cut off 1/2 of the stems.   Cook broccoli in 2 cups boiling water until tender.  Drain, reserving 1 cup of the water.  Take some of the tops, chop lightly and reserve.  Put the chicken stock, onion and reserved water in a pan and bring to a boil.  Add the broccoli and simmer for 5 minutes.  Put through a strainer, vegetable mill or purée in a food processor or blender.  Return to the pot and add the milk or cream and salt and pepper.  Reheat and adjust the seasonings.  Before serving, sprinkle with chopped broccoli tops.

For a thicker soup, before adding the milk, melt 2 tablespoons butter in a large pot, stir in 2 tablespoons flour, and cook for a few minutes until smooth.  Slowly add the milk or cream and salt and pepper.  Then add the broccoli purée and reheat until thickened.