In a large pot, heat 2 tablespoons of olive oil and 2 tablespoons of butter over medium heat until melted and bubbly. Add 1 finely chopped onion, cooking for about 5 minutes until soft and translucent.

Introduce 12 peeled garlic cloves to the onion mixture, sautéing for an additional 2-3 minutes.

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

Remove the thyme and bay leaves from the pot. Taste the soup and season with salt and freshly cracked pepper.

In a small bowl, whisk together 3 egg yolks and ½ cup of grated Parmesan cheese. Temper the egg mixture by slowly adding a ladle of hot soup while whisking continuously.

Gradually return the tempered egg mixture back into the pot, whisking continuously. Allow the soup to gently simmer for an additional 5 minutes.

Ladle the warm soup into bowls and serve hot with slices of crusty bread for dipping. If desired, garnish with freshly chopped parsley.