Preheat your oven to 400°F (200°C). Slice the top off a whole head of garlic, drizzle it with olive oil, and wrap it in aluminum foil. Place the wrapped garlic on a baking tray and roast for 30-40 minutes, until the cloves are soft, golden, and fragrant.

While your garlic is roasting, grab a large pot to start making the soup. Pour in your chicken stock and bring it to a gentle boil over medium heat. Stir in a pinch of salt and dried sage, then reduce the heat to low and let it simmer.

Once the garlic is out of the oven and cool enough to handle, squeeze the roasted cloves into a bowl to create a smooth paste.

In a separate bowl, combine a fresh egg yolk with Dijon mustard and whisk them together until fully blended. Gradually drizzle in olive oil while continuously whisking to create a creamy emulsion.

Return to your simmering stock and slowly whisk in the mashed roasted garlic, ensuring it blends evenly. Continue to whisk the creamy emulsion into the hot stock until fully incorporated.

Once everything is well combined and heated through, ladle the garlic-infused broth into bowls and, if desired, top with a poached egg.