Heat the olive oil in a large pot over medium heat.
Add the leeks and sprinkle with a pinch of salt. Cook until they soften, about 5 minutes. Add the garlic and ginger and cook for another minute until mix becomes fragrant.
Add the carrots and stir to combine. Add the broth and bring to a simmer. Cook until carrots break apart when pierced with a fork, about 20 minutes.
Using an immersion blender, blender or food processor, puree the soup until smooth. Return to pot.
Stir in milk and cook over low heat for 5 minutes. Taste and adjust seasoning with salt and pepper.
