
Melt the butter in a large pot over medium-high heat. Add the onions, carrots, celery, garlic, thyme, salt, and pepper. Cook the vegetables, until softened, 5-7 minutes.
Add the potatoes and the broth, and bring to a boil for about 5 minutes, then lower the heat to a simmer, cover the pot and continue cooking until the potatoes are fork tender, 25-30 minutes.
Remove the pot from the heat, and stir in the milk.
Using an immersion blender, carefully blend the soup until smooth. Alternatively, you can transfer the soup to a blender in batches and blend until all the soup is smooth.
Serve the soup with sour cream and chives, if desired.