Chop the potatoes into cubes and break apart the garlic head. Place on a large cookie sheet and drizzle olive oil over the top. Sprinkle a couple of pinches of salt and pepper over the top. Give it a good mix to evenly coat.
Roast in a 425-degree preheated oven for 25-30 minutes or until the potatoes are cooked through. Remove from the oven and set aside.
When the garlic cloves are cool enough, squeeze out the roasted garlic from the skins. Set aside.
To make the soup
In a large soup pot over medium-low heat add about 2 tablespoons of olive oil. Add the onions and saute until they become translucent. About 3 minutes. Add the potatoes and garlic, bay leaves, thyme, salt, and pepper. Stir to combine and add the chicken stock. Simmer over medium-low heat for 20-30 minutes.
Remove from the heat and take out the bay leaves. With an immersion blender or in a regular blender (in small batches) blend the soup until smooth. (If using a blender, put the soup back in the pot). Stir in the cheese and the parsley. Let the cheese melt. Serve immediately.