Peel the garlic cloves and toss them with a tablespoon of olive oil, then spread on a baking sheet. Roast in the oven at 400°F (200°C) until golden and fragrant, about 20-25 minutes.
While the garlic roasts, trim the leeks, slice them thinly, and rinse thoroughly in cold water to remove grit. Drain well.
Heat the remaining olive oil in a large pot over medium heat. Add the sliced leeks and cook, stirring occasionally, until they soften and turn translucent, about 8-10 minutes.
Add the roasted garlic cloves to the pot and cook for another minute, stirring to release their aroma.
Pour in enough vegetable broth to cover the leeks and garlic, then bring the mixture to a gentle simmer. Cook uncovered for about 15-20 minutes, until the flavors meld and the vegetables are tender.
Remove the pot from heat and use an immersion blender to purée the soup directly in the pot until smooth and silky. Be careful as the liquid will be hot and bubbling.
Taste the soup and adjust seasoning with salt and pepper as needed. If desired, swirl in a little cream for extra richness.
Serve the soup hot, garnished with fresh herbs or a drizzle of olive oil if desired.
