Preheat oven to 375 degrees F. Trim the tops of the garlic to expose the tips of the cloves. Place the garlic cut side up in a small baking dish. Drizzle with 2 tsp. of the olive oil. Cover tightly and bake 45-55 minutes, or until the garlic is tender. Cool until safe enough to handle. Pop the cloves out of their skins. Heat the remaining oil in a soup pot. Add the onion and garlic and cook 3-4 minutes. Stir in the flour until well-combined. Slowly pour in the stock, stirring steadily. Add potato and thyme and bring to soup to a simmer. Cook 20 minutes, until the potato is tender. Puree the mixture in a food processor or blender. Return the soup to the pot and bring back to a simmer. Season with salt and pepper. Pour into bowls. Top with cheese, garnish with parsley and serve.