In a large pot, combine 2 tablespoons of olive oil and 2 tablespoons of butter over medium heat. Let them melt together until they shimmer but do not brown.

Add 1 finely chopped onion to the pot and sauté for about 5 minutes until it softens and becomes translucent.

Introduce 10 peeled garlic cloves to the pot, cooking them for 2 to 3 minutes until they become fragrant.

Pour in 4 cups of chicken or vegetable broth, and add 1 teaspoon of fresh thyme and 2 bay leaves. Bring to a gentle boil, then reduce to a simmer for 30 minutes.

Remove the thyme and bay leaves. Taste the soup, and add salt and pepper as needed.

In a small bowl, whisk together 2 egg yolks and ½ cup of grated Parmesan cheese, then temper by slowly whisking in a ladle of hot soup.

Return the egg mixture back to the soup while stirring gently.

Let the soup simmer on low heat for an additional 5 minutes, stirring gently to achieve the desired texture.

Ladle into bowls and serve hot with crusty bread, garnished with fresh parsley if desired.