In a large pot add cubed potatoes and fill with enough cold water to cover potatoes. Bring to a boil, reduce heat and allow to simmer until fork tender, about 15-20 minutes.
Drain water and mash potatoes with butter, salt, and pepper, adding more salt and pepper to taste, if desired.
Preheat oven to 400°F. Spray a 12-cup muffin tin with non-stick cooking spray.
In a large bowl, combine mashed potatoes, cheddar cheese, broccoli, eggs, chives, garlic, salt, and pepper.
Evenly divide potato mixture into the 12 muffin cups.
Bake for 30-35 minutes, or until potato puffs are set and tops are browned.
Remove muffin tin to a wire rack to cool for about 5 minutes. Carefully remove potato puffs from tin to serving platter. Top with sour cream and additional chopped chives. Serve immediately.
Store leftovers in the refrigerator.