Remove broccoli leaves and trim stem. Set aside 12 broccoli florets. Coarsely chop the remaining broccoli.
Melt butter in a large saucepan. Add the garlic and onion, cover and simmer for 5 minutes until soften. Add the paprika, potato, broccoli and broth. Bring to a boil.
Cover and simmer for 30 minutes. Cool slightly.
Puree in blender, and then return the soup to saucepan. Stir in milk, parsley and season. Reheat
Meanwhile, blanch the broccoli florets in boiling water for 2 to 3 minutes, then drain.
Serve into 4 soup bowls and garnish with broccoli florets. Serve immediately.