Step 1

Heat the oil in a large pot over medium heat. Add the carrots, celery and onions and cook until the onions are soft and translucent, 3 to 5 minutes. Add the thyme and garlic and cook until fragrant, 45 to 60 seconds. Season with salt and pepper. Sprinkle the flour over and cook, stirring, for 2 minutes. Gradually whisk in the stock, and then the milk. Add the potatoes and bring the soup to a boil over high heat. Decrease the heat to low and simmer until the potatoes are tender, about 20 minutes.

Step 2

Using an immersion blender, puree the soup; leave it coarse and chunky if you prefer a more rustic soup, or puree until smooth for a more elegant soup. Add the cheese, about 1/3 cup at a time, stirring after each addition until melted and smooth. Taste and adjust for seasoning with salt and pepper.

Step 3

To serve, ladle the soup into warmed bowls. Sprinkle with chives and serve immediately.