In a large pot, melt duck fat (or olive oil) and fry the onion for 2 minutes. Add the peeled/ sliced head of garlic and continue frying for 2 more minutes. The onion & garlic must not brown. Add flour, stir and pour the chicken stock in the pot. Bring to a soft boil, season with salt and pepper, add sprigs of thyme. Cover and leave to simmer for 20 minutes.
In a small frying pan, heat 1 tbsp olive oil and fry sliced garlic until golden and slightly crispy. Drain on paper towel and set aside.
Purée soup using a hand blender, or in batches in a regular blender. Return soup to pot and switch on medium heat.
Separate eggs. Beat the egg whites in a small bowl and whisk continuously into the soup. You should see thin strands in the soup. Take immediately off the heat. Whisk egg yolks with vinegar and dilute mixture into the soup, stir constantly to avoid any curdling. Sprinkle with fried garlic and drizzle with a few drops of olive oil (optional). Serve immediately with thinly t