Roast the garlic. Preheat the oven to 400 degrees F. Cut the basal end (the one with the roots) off the heads of garlic and wrap all three heads in one big sheet of tinfoil, covering completely and tightly. Roast for 40 minutes and remove. Let cool before squeezing the softened garlic out of its papery shells and setting aside.
Heat the olive oil and butter in a soup or stock pot over medium heat and saute the onion until softened, about 4 minutes. Add the fresh herbs and the cubed potatoes and saute for another 3-4 minutes.
Add the stock and bring to a simmer and cook, covered over, low heat for 25-30 minutes, until the potatoes are cooked all the way through.
Add the roasted garlic cloves, cream, salt and pepper and puree until smooth in the pot using an immersion blender or in batches in a blender or food process.
Taste and adjust the seasonings before serving warm with crusty bread or croutons and a sprinkling of fresh herbs.