Prep leeks by slicing off the stems and green leaves, keeping the white and light green parts. Cut leeks in half lengthwise, then chop across.
Rinse chopped leeks under cold water in a colander to remove dirt and debris.
Heat olive oil in a large pot or Dutch oven over medium heat. Add leeks and sauté for 8 to 10 minutes until softened but not browned. Stir in minced garlic and cook for another minute.
Add diced potatoes, kosher salt, bay leaf, thyme sprigs, and vegetable broth. Bring to a boil over high heat, then reduce to low. Cover and simmer for 15 to 20 minutes until potatoes are tender.
Remove bay leaf and thyme sprigs. Use an immersion blender to blend soup until smooth and creamy, or blend in batches in a blender for desired texture.
Serve hot, garnished with freshly chopped chives and black pepper.
