Preheat your oven to 400°F. Trim the tops of the garlic heads and place them cut-side up in aluminum foil. Drizzle with olive oil, then wrap them into small foil packages. Put the garlic in a baking dish and roast for about 45 minutes, until softened. Once roasted, unwrap and let the garlic cool.
In a medium pot, melt the butter over medium heat. Add the onion, salt, and pepper, and sauté for about 3 minutes until the onion turns translucent.
Pour in the white wine and sprinkle in the Italian seasoning, letting it simmer for a minute. Add the chicken broth and potatoes. Bring to a boil, then reduce the heat, cover, and let it simmer for 15 minutes, or until the potatoes are fork-tender.
Once the garlic is cool, squeeze the soft cloves from the skins and add them to the pot. Use an immersion blender (or a regular blender) to purée the soup until it's smooth and creamy.
Stir in the heavy cream and grated parmesan, adjusting the seasoning if needed with extra salt and pepper.
Serve warm, topped with croutons, a sprinkle of fresh parsley, and a generous amount of extra parmesan.