In a small food processor, blend garlic cloves and fresh cilantro until finely ground into a paste.
In a large heavy cooking pot, heat 3 tablespoon olive oil over medium-high heat until shimmering but not smoking. Add the garlic and cilantro mixture and the chopped leeks. Cook, tossing regularly, until leeks are tender.
Add potatoes, spices, and a generous dash of salt and pepper. Toss to coat.
Add bay leaves and vegetable broth.
Bring to a boil for 5 minutes, then reduce heat to medium-low. Cover and let simmer another 15 minutes or so until the potatoes are tender and fully cooked.
Turn off heat. Fish the bay leaves out. Using an immersion blender, blend the potato leek to your liking (I like to leave some chunks, others like it fully blended to a smooth and creamy consistency).
Place the pot back on stove to heat the soup through over medium heat, stirring. Taste and adjust seasoning.
Transfer soup to serving bowls. Add a generous drizzle of good olive oil. Serve with lemon wedges (a splash of fresh lemon juice is a great addition). Enjoy with your favorite crusty bread.