Melt butter in a large pot over medium heat. Add leeks and cook until soft and translucent, about 5 minutes. Stir in pepper, salt, and coriander.
Reserve about 1/4 cup of the smallest broccoli florets. Add remaining broccoli to the leeks and cook until bright green, about 5 minutes. Pour in chicken stock and bring to a boil. Reduce the heat, cover, and simmer until broccoli is very tender, 10 to 15 minutes.
Purée soup with an immersion blender until smooth. Stir in reserved broccoli florets and bring to a simmer over medium-low heat, stirring often. Simmer until broccoli is tender, 5 to 7 minutes.
Remove from the heat and stir in evaporated milk. Serve hot.