Melt 2 tablespoons of unsalted butter with 1 tablespoon of olive oil in a large Dutch oven over medium-low heat. Add the peeled whole garlic cloves and sliced yellow onions. Cook slowly for about 15 minutes, stirring frequently. You want the garlic and onions to become translucent, soft, and lightly golden, never dark brown or burnt.

Pour in 0.5 cup of dry white wine to deglaze the pot, scraping up any delicious browned bits from the bottom. Allow the wine to reduce by half for about 3 minutes. Add the sprigs of fresh thyme and 2 bay leaves.

Pour in 6 cups of rich chicken broth or vegetable stock. Season gently with sea salt, freshly cracked black pepper, and a tiny pinch of freshly grated nutmeg. Bring the mixture to a gentle boil, then lower the heat, cover, and let it simmer softly for 20 minutes so the garlic completely softens.

Remove the bay leaves and thyme stems. Use an immersion blender to puree the soup directly in the pot until smooth, creamy, and velvety. If you prefer a chunkier texture, leave a few whole garlic cloves intact.

In a medium glass bowl, whisk together 2 egg yolks and 0.5 cup of heavy cream. Slowly ladle 1 cup of the warm soup broth into the egg mixture while whisking continuously. This tempers the eggs so they combine smoothly without scrambling.

Stir the tempered egg and cream mixture back into the Dutch oven over low heat. Warm through for 2 minutes without allowing the broth to boil. Ladle into warm bowls, top with toasted garlic bread, parmesan cheese, and fresh parsley, and serve immediately.