Heat the oven to 450°F. On a rimmed baking sheet, toss the potatoes with 2 tablespoons of the oil, rubbing it in with your hands. Season with ½ teaspoon of the salt and ⅛ teaspoon of the pepper, shaking to coat the potatoes evenly. Spread them in a single layer and roast, without turning, until deeply browned on one side, 20 to 25 minutes.
Meanwhile, heat the remaining 1 tablespoon of oil in a large soup pot on medium. Add the onion, celery, and carrots and cook until lightly browned, 5 to 6 minutes. Scrape the roasted potatoes into the pot; then add the bay leaf and broth. Bring the broth to a boil over high heat. Reduce the heat to medium and simmer until the potatoes are very tender, 10 to 15 minutes. Using tongs or a slotted spoon, fish out and set aside about 1½ cups of potato pieces. Discard the bay leaf and puree the soup until smooth with a stick blender or an upright blender.
If using an upright blender, return the soup to the pot. Add the cheese over low heat, stirring until melted and smooth. Stir in the reserved potatoes and remaining ¼ teaspoon of salt and ⅛ teaspoon of pepper. Divide the soup among bowls and top each serving with the chives.
Tip: Use smoked cheddar to enhance the roasted flavor. Or for more richness, stir in ½ cup of half-and-half along with the cheese.