Peel away the outer layers of the garlic bulb, but leave the individual skins on the cloves intact.
Using a sharp knife, cut off of the top 1/4 to 1/2 inch of the garlic, exposing the individual cloves. Place the head of garlic on a sheet of aluminum foil, drizzle olive oil over top and sprinkle with a little salt. Then wrap it up, and place inside your oven on the middle baking rack. Roast for 35 to 40 minutes. When the garlic is cool enough to touch, squeeze the entire garlic bulb over a small bowl and set aside.
FOR THE REMAINDER OF THE DISH:
While the garlic is roasting, bring a pot of water to boil. Add the potatoes to the pot and reduce the heat to medium-high. Cook until potatoes are softened and easily fall apart when pricked, about 20 minutes. After 15 minutes, add the onion to the pot to soften for about 5 minutes. Drain mixture and set aside.
In a blender or food processor, add chicken broth, heavy cream, roasted garlic, potatoes and onions, salt and black pepper. If using a blender, remove the plastic piece in the lid, and place a towel on top to let steam escape.
Process mixture until smooth.
Serve warm with a side of bread or in a bread bowl, and sprinkle with chives on top, if desired.