Heat the chicken stock and sage in a large Dutch oven or stock pot. Bring to a simmer and then simmer very gently while you prep your garlic.

Remove the skins from the garlic cloves and slice them in half lengthwise. Remove the little embryonic shoot.

Bring a small saucepan of water to a boil and add the garlic cloves. Boil for 3-4 minutes. Drain the cloves.

Use the back of a fork to mash the softened garlic until finely mashed. Add the mashed garlic to the stock and continue to gently simmer for 10 minutes.

Put the egg yolk, mustard, salt, and oil in a small jar. Blend with an immersion blender, gently lifting the blender slightly to emulsify.

If the mayonnaise does not thicken, add the reserved egg white and blend again.

Optional: Strain the soup for a velvety smooth texture, and return strained soup to the pot.

Take a ladle-ful of the hot soup and stir it into your mayonnaise to temper it. Then immediately stir the mayonnaise into the soup pot, whisking as you add it.

Bring the soup back on the stove and heat, but do not let it boil.