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 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. Remove from heat and mix in the condensed milk. Serve hot.