Heat the olive oil in a large pot over medium heat. Add the sliced leeks and minced garlic, then cook for 5 minutes until the leeks soften.
Add the cauliflower florets, vegetable broth, salt, and black pepper to the pot. Bring the mixture to a boil, then reduce the heat and simmer for 15 minutes until the cauliflower is tender.
Remove the pot from the heat. Use an immersion blender to puree the soup until it reaches a smooth consistency, or transfer it in batches to a countertop blender.
Return the pot to low heat and stir in the almond milk. Warm the soup for 3 minutes, stirring occasionally, then taste and adjust salt if needed.
Ladle the soup into bowls and top each serving with chopped fresh chives.