Trim the leeks, removing the dark green leaves and stem, and slice the remaining white and light green portions in half lengthwise. Chop into smaller pieces and rinse thoroughly in a colander under cold water to remove dirt.

Heat the olive oil in a large pot or Dutch oven over medium heat. Add the prepared leeks and sauté for 8–10 minutes until softened but not browned. Stir in the minced garlic and cook for an additional minute.

Add the diced potatoes, kosher salt, bay leaf, thyme sprigs, and vegetable broth. Bring the mixture to a boil over high heat, then lower to a simmer. Cover and cook for 15–20 minutes, or until the potatoes are tender when pierced with a fork.

Remove and discard the bay leaf and thyme sprigs. Using an immersion blender, purée the soup to your desired consistency. For chunkier soup, blend partially or in sections. For a smooth texture, blend completely. Alternatively, you can use a high-powered blender to purée the soup in batches.

Ladle the soup into bowls and garnish with freshly chopped chives and ground black pepper before serving.