Combine chicken broth, onions, broccoli, thyme, bay leaf and garlic cloves. Bring to a boil. Simmer, partially covered, for 10 minutes.
In a small saucepan, melt butter. Stir in flour, salt and pepper. Add milk gradually, stirring constantly until all milk is added; mixture will be lumpy at first, but will smooth out as you keep stirring. Cook, stirring occasionally, till mixture bubbles
Remove and discard bay leaf from broccoli/broth mixture. Purée in batches in blender or food processor for 30 seconds, or until very smooth. Transfer to large bowl. Add milk mixture, stirring until well combined. Adjust seasoning. Serve hot.