Step 1

Cook leeks and oil in a large heavy pot over medium-high heat, covered and stirring occasionally, until the leeks are slightly tender, 5 to 6 minutes. Stir in garlic, thyme and salt; reduce heat to medium and cook, covered and stirring occasionally, until the leeks are very soft, 10 to 12 minutes.

Step 2

Add broth, russet potatoes and red potatoes to the leek mixture; bring to a simmer over high heat. Cover, reduce heat to medium and cook, undisturbed, until the russet potatoes start to break down and the soup thickens slightly, about 30 minutes. Stir in pepper. Ladle evenly into 6 bowls; sprinkle with chives.