Swapping half the potatoes for cauliflower gives this mash a lighter texture and slashes the calories and carbs. Whole-milk yogurt ensures it is silky smooth and adds a bright flavor hit, too.
Put potatoes in a large Dutch oven, then add garlic and cauliflower. Pour broth over mixture. Cover and bring to a boil over high. Reduce heat to medium-low; simmer until vegetables are tender, about 12 minutes. Drain.
Transfer half of cauliflower mixture to a food processor. Secure lid on food processor, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, 45 seconds to 1 minute. Transfer to a serving bowl. Process remaining cauliflower mixture in food processor, and process until smooth, 45 seconds to 1 minute. Add yogurt, butter, salt, and pepper; process until smooth, about 30 seconds. Add to serving bowl; stir to combine. Garnish with chives and additional pepper.
This can be made two days ahead and chilled, covered. Reheat on the stovetop over low heat or in the microwave, covered.