Melt butter in a large pot, and cook the leeks over medium heat until soft and translucent, about 5 minutes. Stir in salt, pepper, and coriander. Reserve about 1/4 cup of small broccoli florets, and cook the rest of the broccoli with the leeks until the broccoli is bright green, about 5 more minutes.
Pour in the chicken stock, bring the soup to a boil, cover, then simmer until the broccoli is very tender, 10 to 15 minutes.
Pour the soup into a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to puree. Puree in batches until smooth and pour into a clean pot. Alternately, you can use a stick blender and puree the soup right in the cooking pot.
Return the blended soup to the pot, stir in the reserved broccoli florets, and bring to a simmer over medium-low heat, stirring often. Simmer until the broccoli florets are tender, 5 to 7 minutes.
