Heat 1 tbsp olive oil in a large pot over medium heat. Add the onion and cook 4-5 minutes until soft. Add the garlic and cook 30 seconds until fragrant.
Add the cauliflower, broth, salt and pepper. Bring to a boil, then reduce the heat to low, cover and simmer 12-15 minutes until the cauliflower is very tender.
Stir in the beans and simmer uncovered for 2 minutes.
Remove from the heat and blend with an immersion blender until completely smooth, 1-2 minutes. Or blend in batches in a stand blender, venting the lid.
Stir in the milk and lemon juice. Return to low heat and warm for 2 minutes without boiling.
Taste and adjust the salt and pepper. Ladle into bowls and top with chives and a drizzle of the remaining olive oil.