Preheat the oven to 350°F. Cut off the root end of each garlic clove and lightly smash with the side of a chef's knife to loosen the skin; peel easily.

Place the peeled garlic cloves in a small glass baking dish. Drizzle with 2 tablespoons olive oil, season with a pinch each of salt and pepper, and toss to coat.

Cover the dish tightly with a lid or aluminum foil and roast until the garlic is golden brown and very tender, about 45 minutes. Transfer to a bowl and let cool. (If making a day ahead, refrigerate the cooled cloves in a sealed container.)

In a heavy, large saucepan over medium-high heat, melt 2 tablespoons butter. Add the chopped onions and thyme; cook, stirring occasionally, until the onions are translucent, about 5 minutes.

Add the roasted garlic cloves and the 18 raw garlic cloves (minced or thinly sliced) and cook for 2 minutes, stirring, to release their fragrance.

Add the russet potato chunks and pour in the broth. Bring to a simmer, cover, and cook until the garlic and potato are very tender, about 20 minutes.

Using an immersion blender, puree the soup directly in the pot until smooth. (Alternatively, working in batches, transfer to a blender and puree carefully, then return to the pot.) If you added potato chunks, you can leave a few in for texture or puree completely.

Stir in the heavy cream and reheat the soup over low heat until warmed through, but do not boil. Season with 1/2 teaspoon salt and 1/2 teaspoon pepper; adjust to taste.

Divide the grated Parmesan cheese among four soup bowls (about 2 tablespoons per bowl). Ladle the hot soup over the cheese. Squeeze one Meyer lemon wedge into each bowl and serve immediately.

Garnish each serving with additional Parmesan, toasted croutons, sauteed minced garlic, or Parmesan crisps if desired.

Preheat the oven to 400°F. Line a baking sheet with parchment or a silicone mat. Drop heaping tablespoons of grated Parmesan onto the sheet, spacing them about 1/2 inch apart. Flatten each mound slightly with the back of a spoon.

Bake until the cheese melts, bubbles, and turns golden brown, 3 to 10 minutes (ovens vary; check after 5 minutes). Let cool on the sheet for 1 minute, then carefully transfer with a spatula to a wire rack. Serve alongside the soup.