Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper. Place the cauliflower florets and chopped yellow onion onto the baking sheet. Drizzle with 2 1/2 tablespoons of olive oil, sea salt, black pepper, and thyme. Toss thoroughly so every piece is evenly glistening.

Drizzle the cut top of the whole garlic head with the remaining 1/2 tablespoon of olive oil, wrap tightly in aluminum foil, and place directly on the baking sheet alongside the cauliflower.

Roast for 25 to 30 minutes, tossing the florets halfway through, until the cauliflower edges are deeply golden-brown and caramelized, and the garlic cloves inside the foil are soft, golden, and sweet. Set aside a handful of the crispiest florets for bowl garnishing.

Transfer the roasted cauliflower and onions into a large Dutch oven or soup pot over medium heat. Squeeze the soft roasted garlic cloves out of their papery skins directly into the pot. Pour in 3 1/2 cups of the broth.

Bring to a gentle simmer for 5 minutes, allowing all the caramelized roasting flavors to marry together.

Using a high-powered immersion blender (or transferring carefully in batches to a stand blender), puree the soup on high speed for a full 2 to 3 minutes until completely uniform, ultra-glossy, and velvety smooth without a single lump. Add the remaining 1/2 cup of broth if you prefer a lighter texture.

Turn the heat to low. Stir in the heavy cream, freshly grated Parmigiano Reggiano, lemon juice, and a pinch of ground nutmeg. Simmer very gently for 2 minutes until the cheese is completely melted and incorporated.

Taste and adjust seasoning with a pinch more sea salt or black pepper if desired.

Ladle the steaming velvety soup into shallow ceramic bowls. Top with reserved crispy roasted florets, crunchy herb sourdough croutons, a swirl of extra virgin olive oil, freshly ground black pepper, and thyme leaves. Serve warm with crusty sourdough bread!