Preheat oven to 375º F.
Wash and quarter potatoes, keeping them immersed in cold, salted water as you work.
Toss garlic clove in olive oil and set on baking sheet, roast until garlic has turned golden brown, about 20 minutes.
Put potatoes in a large pot with a lid with salted, cold water. Cover and bring pot to a boil over a high heat and then reduce to medium boil for 15 to 20 minutes, or until potatoes easily pierce with a sharp knife. Drain through a colander.
Remove roasted garlic from the oven. Using the flat side of a chef’s knife crush the garlic and chop very finely.
Transfer the potatoes and garlic to an electric mixer fitted with a paddle. Mix at low speed to break up potatoes, then slowly add the chicken broth and two tablespoons of the butter, one teaspoon of salt and a few grinds of pepper.
Scrape down the side of the bowl down, beat in more balance of butter, additional broth if needed for consistency and chives. Adjust seasoning to taste spoon.