Sauté the Onion and Garlic. Heat the olive oil and butter in a large pot over medium heat. Add the chopped onion and sauté until softened, about 5 minutes. Add the peeled garlic cloves and cook for an additional 2-3 minutes, stirring frequently to prevent burning.

Add the Broth and Herbs. Pour in the broth and add the thyme sprigs and bay leaves. Bring the soup to a boil, then reduce the heat and let it simmer gently for 30 minutes, allowing the garlic to soften and infuse the broth with flavor.

Remove Herbs and Season. After 30 minutes, remove the thyme sprigs and bay leaves. Season the soup with salt and pepper to taste.

Temper the Egg Yolks. In a small bowl, whisk together the egg yolks and Parmesan cheese. To temper the eggs and avoid curdling, slowly whisk a ladle of hot soup into the egg mixture.

Gradually whisk this mixture back into the soup pot.

Thicken the Soup. Simmer the soup for another 5 minutes, stirring continuously as it thickens slightly.

Serve. Ladle the hot soup into bowls and serve with crusty bread on the side. Optionally, garnish with fresh parsley for added flavor and color.