Melt butter in a heavy, large saucepan over medium-high heat.
Add the onions and thyme and cook until onions are translucent, about 5 minutes.
Add the roasted garlic and the 18 raw garlic cloves and cook a couple of minutes to release some of the raw garlic oils.
If you're adding the russet potato chunks, add now as well.
Add chicken or vegetable broth; cover and simmer until garlic is very tender, about 20 minutes. If you're making the Parmesan Cheese Crisps, make them now while the soup is simmering.
If you added the russet potato chunks, remove them after the 20 minute simmer and place in a small bowl or on a plate while you puree the rest of the ingredients. Working in batches, puree soup in a blender until smooth or puree with an immersion blender. Return potato chunks to the creamed soup.
Return soup to the saucepan, add cream, or whatever milk you are using, and bring to a very low simmer just to reheat, being careful not to curdle the milk. Add 1/2 teaspoon salt and 1/2 teaspoon freshly ground pepper. Taste and add more to your liking.
Divide the grated 1/2 cup of Parmesan cheese among 4 bowls and ladle soup over. Each bowl will get about 2 tablespoons of cheese.
Squeeze juice of 1 lemon wedge into each bowl and serve.
Serve in individual bowls garnished with more grated Parmesan, Parmesan Crips or toasted croutons, or the additional minced sauteed garlic.
How to make Parmesan Crisp garnish: Heat your oven to 400F degrees, Pour a heaping tablespoon of grated Parmesan onto a silicone or parchment lined baking sheet and pat down just a bit. For color or extra flavor, you could sprinkle the cheese mound with herbs, black pepper or red pepper flakes. Repeat with as much Parmesan crisps as desired, spacing the spoonfuls about a 1/2 inch apart. Bake until golden and crisp. Since ovens vary, this time can be anywhere from 3 to 10 minutes (mine finished closer to the 10 minute mark). The cheese will bubble quite a bit, but just keep cooking until the crisps darken. Cool, then using a spatula, carefully scrape the crips off the baking sheet and serve with the soup.