Trim the root ends and dark green leaves off of the leeks. Then cut the leeks (white and light green parts only) in half lengthwise and then cut into ¼-inch wide half moons. Wash the chopped leeks in a bowl of cool water (or in a salad spinner) and drain well.
Heat the olive oil and butter in a Dutch oven or other large heavy pot over medium heat until the butter is melted.
Add the leeks to the pot and sauté until softened, about 6 minutes, stirring occasionally. Add the garlic and cook, stirring, for 30 seconds.
Add the potatoes, 4 cups of broth, dried thyme, bay leaf, salt and pepper to the pot. Stir.
Bring the soup to a boil and then reduce the heat to a low simmer. Cover the pot and simmer, stirring occasionally, until the potatoes are tender when pierced with a fork, about 20 minutes. Remove the pot from the heat.
Remove and discard the bay leaf. Then use an immersion blender to puree the soup until smooth, or transfer it in batches to a counter top blender. If the soup is too thick, add up to 1 cup more broth, a little at a time, until it reaches your desired consistency.
Taste and season with more salt and pepper, if needed. Serve garnished with chopped fresh chives, or as desired.